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贝叶斯推理 - 版本历史
2026-04-19T03:32:39Z
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2026年1月4日 (日) 01:04 77921020
2026-01-04T01:04:33Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年1月4日 (日) 01:04的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l25" >第25行：</td>
<td colspan="2" class="diff-lineno">第25行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <th style="text-align: left; padding: 6px 12px; background-color: #f1f5f9; color: #475569; border-bottom: 1px solid #e2e8f0; width: 40%;">核心公式</th></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <th style="text-align: left; padding: 6px 12px; background-color: #f1f5f9; color: #475569; border-bottom: 1px solid #e2e8f0; width: 40%;">核心公式</th></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #0f172a;"><del class="diffchange diffchange-inline">$$</del>P(D|S) = <del class="diffchange diffchange-inline">\frac{</del>P(S|D)P(D)<del class="diffchange diffchange-inline">}{</del>P(S)<del class="diffchange diffchange-inline">}$$</del></td></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #0f172a;">P(D|S) = <ins class="diffchange diffchange-inline">[</ins>P(S|D) <ins class="diffchange diffchange-inline">× </ins>P(D)<ins class="diffchange diffchange-inline">] / </ins>P(S)</td></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </tr></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50" >第50行：</td>
<td colspan="2" class="diff-lineno">第50行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> 贝叶斯公式是所有医生潜意识里都在使用的工具。在医学语境下，我们通常用 <del class="diffchange diffchange-inline">$</del>D<del class="diffchange diffchange-inline">$ </del>代表<strong>疾病</strong> (Disease)，用 <del class="diffchange diffchange-inline">$</del>S<del class="diffchange diffchange-inline">$ </del>代表<strong>症状/体征</strong> (Symptom/Sign)<del class="diffchange diffchange-inline">：</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> 贝叶斯公式是所有医生潜意识里都在使用的工具。在医学语境下，我们通常用 <ins class="diffchange diffchange-inline"><strong></ins>D<ins class="diffchange diffchange-inline"></strong> </ins>代表<strong>疾病</strong> (Disease)，用 <ins class="diffchange diffchange-inline"><strong></ins>S<ins class="diffchange diffchange-inline"></strong> </ins>代表<strong>症状/体征</strong> (Symptom/Sign)<ins class="diffchange diffchange-inline">。</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <div style="background-color: #f8fafc; padding: 25px; border-radius: 8px; border: 1px solid #e2e8f0; text-align: center; margin: 25px <del class="diffchange diffchange-inline">0</del>;"></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <div style="background-color: #f8fafc; padding: 25px; border-radius: 8px; border: 1px solid #e2e8f0; text-align: center; margin: 25px <ins class="diffchange diffchange-inline">auto; width: fit-content; min-width: 300px</ins>;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <div style="<del class="diffchange diffchange-inline">font</del>-<del class="diffchange diffchange-inline">size</del>: <del class="diffchange diffchange-inline">1.3em</del>; <del class="diffchange diffchange-inline">margin</del>-<del class="diffchange diffchange-inline">bottom</del>: <del class="diffchange diffchange-inline">15px</del>; font-family: 'Times New Roman', serif;"></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <div style="<ins class="diffchange diffchange-inline">display: flex; align</ins>-<ins class="diffchange diffchange-inline">items</ins>: <ins class="diffchange diffchange-inline">center</ins>; <ins class="diffchange diffchange-inline">justify</ins>-<ins class="diffchange diffchange-inline">content</ins>: <ins class="diffchange diffchange-inline">center</ins>; font-family: 'Times New Roman', serif<ins class="diffchange diffchange-inline">; font-size: 1.3em; color: #0f172a</ins>;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <del class="diffchange diffchange-inline">$$</del>P(D|S) = <del class="diffchange diffchange-inline">\frac{</del>P(S|D) <del class="diffchange diffchange-inline">\times </del>P(D)<del class="diffchange diffchange-inline">}{</del>P(S)<del class="diffchange diffchange-inline">}$$</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <ins class="diffchange diffchange-inline"><span style="margin-right: 10px;"></ins>P(D|S) = <ins class="diffchange diffchange-inline"></span></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <div style="display: flex; flex-direction: column; align-items: center;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <span style="border-bottom: 1px solid #0f172a; padding-bottom: 5px; margin-bottom: 5px;"></ins>P(S|D) <ins class="diffchange diffchange-inline">× </ins>P(D)<ins class="diffchange diffchange-inline"></span></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <span></ins>P(S)<ins class="diffchange diffchange-inline"></span></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </div></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.<del class="diffchange diffchange-inline">9em</del>; color: #64748b; border-top: 1px dashed #cbd5e1; padding-top: 15px;<del class="diffchange diffchange-inline">"></del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"> <span style="display</del>: <del class="diffchange diffchange-inline">inline</del>-<del class="diffchange diffchange-inline">block</del>; <del class="diffchange diffchange-inline">padding</del>: <del class="diffchange diffchange-inline">0 10px</del>;"><strong>P(D|S)</strong>: 确诊率 (<del class="diffchange diffchange-inline">后验</del>)</<del class="diffchange diffchange-inline">span</del>></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.<ins class="diffchange diffchange-inline">85em</ins>; color: #64748b; border-top: 1px dashed #cbd5e1; padding-top: 15px; <ins class="diffchange diffchange-inline">margin-top</ins>: <ins class="diffchange diffchange-inline">15px; text</ins>-<ins class="diffchange diffchange-inline">align: left</ins>; <ins class="diffchange diffchange-inline">line-height</ins>: <ins class="diffchange diffchange-inline">1.8</ins>;"<ins class="diffchange diffchange-inline">></ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <<del class="diffchange diffchange-inline">span style="display: inline-block; padding: 0 10px;"</del>><strong>P(S|D)</strong>: 敏感度 (<del class="diffchange diffchange-inline">似然</del>)</<del class="diffchange diffchange-inline">span</del>></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <div</ins>><strong>P(D|S)</strong>: 确诊率 (<ins class="diffchange diffchange-inline">看到症状后的概率</ins>)</<ins class="diffchange diffchange-inline">div</ins>></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <<del class="diffchange diffchange-inline">span style="display: inline-block; padding: 0 10px;"</del>><strong>P(D)</strong>: 基础患病率 (<del class="diffchange diffchange-inline">先验</del>)</<del class="diffchange diffchange-inline">span</del>></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <<ins class="diffchange diffchange-inline">div</ins>><strong>P(S|D)</strong>: 敏感度 (<ins class="diffchange diffchange-inline">有病时出现症状的概率</ins>)</<ins class="diffchange diffchange-inline">div</ins>></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <<ins class="diffchange diffchange-inline">div</ins>><strong>P(D)</strong>: 基础患病率 (<ins class="diffchange diffchange-inline">人群中得病的概率</ins>)</<ins class="diffchange diffchange-inline">div</ins>></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> [[Image:Bayes theorem formula medical]]</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <ul style="list-style-type: none; padding-left: 0;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <ul style="list-style-type: none; padding-left: 0;"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px; border-left: 4px solid #1e40af; padding-left: 15px;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px; border-left: 4px solid #1e40af; padding-left: 15px;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #1e40af;">1. 先验概率 <del class="diffchange diffchange-inline">$</del>P(D)<del class="diffchange diffchange-inline">$</del>：</strong> </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #1e40af;">1. 先验概率 P(D)：</strong> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验前概率]]</strong>。在还没做检查前，这个病人患病的可能性有多大？这取决于<strong>流行病学数据</strong>（如：该年龄段人群的基础患病率）。</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验前概率]]</strong>。在还没做检查前，这个病人患病的可能性有多大？这取决于<strong>流行病学数据</strong>（如：该年龄段人群的基础患病率）。</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px; border-left: 4px solid #b91c1c; padding-left: 15px;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px; border-left: 4px solid #b91c1c; padding-left: 15px;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #b91c1c;">2. 似然度 <del class="diffchange diffchange-inline">$</del>P(S|D)<del class="diffchange diffchange-inline">$</del>：</strong> </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #b91c1c;">2. 似然度 P(S|D)：</strong> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">如果病人真有这个病，出现这个症状（或检查阳性）的概率是多少？这对应于诊断试验的<strong>[[敏感度]]</strong>。</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">如果病人真有这个病，出现这个症状（或检查阳性）的概率是多少？这对应于诊断试验的<strong>[[敏感度]]</strong>。</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px; border-left: 4px solid #0f172a; padding-left: 15px;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px; border-left: 4px solid #0f172a; padding-left: 15px;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #0f172a;">3. 后验概率 <del class="diffchange diffchange-inline">$</del>P(D|S)<del class="diffchange diffchange-inline">$</del>：</strong> </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #0f172a;">3. 后验概率 P(D|S)：</strong> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验后概率]]</strong>。看到检查结果阳性后，病人真正患病的概率。这才是医生和 AI 最终要输出的结论。</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验后概率]]</strong>。看到检查结果阳性后，病人真正患病的概率。这才是医生和 AI 最终要输出的结论。</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l82" >第82行：</td>
<td colspan="2" class="diff-lineno">第88行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> 贝叶斯推理揭示了一个反直觉的医学现象：<strong>如果一种病非常罕见（先验概率 <del class="diffchange diffchange-inline">$</del>P(D)<del class="diffchange diffchange-inline">$ </del>极低），即使检查手段非常准确（敏感度 <del class="diffchange diffchange-inline">$</del>P(S|D)<del class="diffchange diffchange-inline">$ </del>高），阳性结果也很有可能是误诊（假阳性）。</strong></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> 贝叶斯推理揭示了一个反直觉的医学现象：<strong>如果一种病非常罕见（先验概率 P(D) 极低），即使检查手段非常准确（敏感度 P(S|D) 高），阳性结果也很有可能是误诊（假阳性）。</strong></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><strong>AI 医生的启示：</strong> 当“智慧医生”看到一个年轻人（低风险）出现某种症状时，它不应直接跳到罕见癌症的诊断，因为先验概率太低；除非有极强的证据（极高的似然比）来扭转这一判断。这是防止 AI 出现“大惊小怪”误诊的关键逻辑。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><strong>AI 医生的启示：</strong> 当“智慧医生”看到一个年轻人（低风险）出现某种症状时，它不应直接跳到罕见癌症的诊断，因为先验概率太低；除非有极强的证据（极高的似然比）来扭转这一判断。这是防止 AI 出现“大惊小怪”误诊的关键逻辑。</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td></tr>
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77921020
https://www.yiliao.com/index.php?title=%E8%B4%9D%E5%8F%B6%E6%96%AF%E6%8E%A8%E7%90%86&diff=312632&oldid=prev
2026年1月4日 (日) 01:01 77921020
2026-01-04T01:01:31Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年1月4日 (日) 01:01的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17" >第17行：</td>
<td colspan="2" class="diff-lineno">第17行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="padding: 25px; text-align: center; background-color: #f8fafc;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="padding: 25px; text-align: center; background-color: #f8fafc;"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="display: inline-block; background: #ffffff; border: 1px solid #e2e8f0; border-radius: 12px; padding: 20px; box-shadow: 0 4px 10px rgba(0,0,0,0.04);"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="display: inline-block; background: #ffffff; border: 1px solid #e2e8f0; border-radius: 12px; padding: 20px; box-shadow: 0 4px 10px rgba(0,0,0,0.04);"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> [[Image:Bayes_Theorem_Icon.png|100px|概率更新<del class="diffchange diffchange-inline">|链接=Special:FilePath/Bayes_Theorem_Icon.png</del>]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> [[Image:Bayes_Theorem_Icon.png|100px|概率更新]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.8em; color: #64748b; margin-top: 12px; font-weight: 600;">临床诊断的数学本质</div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.8em; color: #64748b; margin-top: 12px; font-weight: 600;">临床诊断的数学本质</div></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l25" >第25行：</td>
<td colspan="2" class="diff-lineno">第25行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <th style="text-align: left; padding: 6px 12px; background-color: #f1f5f9; color: #475569; border-bottom: 1px solid #e2e8f0; width: 40%;">核心公式</th></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <th style="text-align: left; padding: 6px 12px; background-color: #f1f5f9; color: #475569; border-bottom: 1px solid #e2e8f0; width: 40%;">核心公式</th></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #0f172a;">$$P(<del class="diffchange diffchange-inline">A</del>|<del class="diffchange diffchange-inline">B</del>) = \frac{P(<del class="diffchange diffchange-inline">B</del>|<del class="diffchange diffchange-inline">A</del>)P(<del class="diffchange diffchange-inline">A</del>)}{P(<del class="diffchange diffchange-inline">B</del>)}$$</td></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #0f172a;">$$P(<ins class="diffchange diffchange-inline">D</ins>|<ins class="diffchange diffchange-inline">S</ins>) = \frac{P(<ins class="diffchange diffchange-inline">S</ins>|<ins class="diffchange diffchange-inline">D</ins>)P(<ins class="diffchange diffchange-inline">D</ins>)}{P(<ins class="diffchange diffchange-inline">S</ins>)}$$</td></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </tr></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </tr></div></td></tr>
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<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50" >第50行：</td>
<td colspan="2" class="diff-lineno">第50行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <del class="diffchange diffchange-inline">贝叶斯公式是所有医生潜意识里都在使用的工具，哪怕他们自己没有意识到：</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <ins class="diffchange diffchange-inline">贝叶斯公式是所有医生潜意识里都在使用的工具。在医学语境下，我们通常用 $D$ 代表<strong>疾病</strong> (Disease)，用 $S$ 代表<strong>症状/体征</strong> (Symptom/Sign)：</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <div style="background-color: #f8fafc; padding: <del class="diffchange diffchange-inline">20px</del>; border-radius: 8px; border: 1px solid #e2e8f0; text-align: center; margin: <del class="diffchange diffchange-inline">20px </del>0;"></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <div style="background-color: #f8fafc; padding: <ins class="diffchange diffchange-inline">25px</ins>; border-radius: 8px; border: 1px solid #e2e8f0; text-align: center; margin: <ins class="diffchange diffchange-inline">25px </ins>0;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> (<del class="diffchange diffchange-inline">敏感度</del>) <del class="diffchange diffchange-inline"> (基础患病率)</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <ins class="diffchange diffchange-inline"><div style="font-size: 1.3em; margin-bottom: 15px; font-family: 'Times New Roman', serif;"></ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"> </del>P(<del class="diffchange diffchange-inline">症状</del>|<del class="diffchange diffchange-inline">有病</del>) <del class="diffchange diffchange-inline"> × </del>P(<del class="diffchange diffchange-inline">有病</del>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> $$P</ins>(<ins class="diffchange diffchange-inline">D|S</ins>) <ins class="diffchange diffchange-inline">= \frac{</ins>P(<ins class="diffchange diffchange-inline">S</ins>|<ins class="diffchange diffchange-inline">D</ins>) <ins class="diffchange diffchange-inline">\times </ins>P(<ins class="diffchange diffchange-inline">D</ins>)<ins class="diffchange diffchange-inline">}{</ins>P(<ins class="diffchange diffchange-inline">S</ins>)<ins class="diffchange diffchange-inline">}$$</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"> </del>P(<del class="diffchange diffchange-inline">确诊率</del>) <del class="diffchange diffchange-inline"> </del>= <del class="diffchange diffchange-inline"> </del>------<del class="diffchange diffchange-inline">----------------------------</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </div></ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"> </del>P(<del class="diffchange diffchange-inline">出现症状的总概率</del>)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <div style</ins>=<ins class="diffchange diffchange-inline">"font</ins>-<ins class="diffchange diffchange-inline">size: 0.9em; color: #64748b; border</ins>-<ins class="diffchange diffchange-inline">top: 1px dashed #cbd5e1; padding</ins>-<ins class="diffchange diffchange-inline">top: 15px;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <span style="display: inline</ins>-<ins class="diffchange diffchange-inline">block; padding: 0 10px;"><strong>P(D|S)</strong>: 确诊率 (后验)</span></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <span style="display: inline</ins>-<ins class="diffchange diffchange-inline">block; padding: 0 10px;"><strong>P(S|D)</strong>: 敏感度 (似然)</span></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> <span style="display: inline</ins>-<ins class="diffchange diffchange-inline">block; padding: 0 10px;"><strong></ins>P(<ins class="diffchange diffchange-inline">D</ins>)<ins class="diffchange diffchange-inline"></strong>: 基础患病率 (先验)</span></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </div></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[Image of Bayesian inference formula]</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <ul style="list-style-type: none; padding-left: 0;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <ul style="list-style-type: none; padding-left: 0;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px;"></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom<ins class="diffchange diffchange-inline">: 15px; border-left: 4px solid #1e40af; padding-left</ins>: 15px;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #1e40af;">1. 先验概率 $P(<del class="diffchange diffchange-inline">\text{病}</del>)$：</strong> </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #1e40af;">1. 先验概率 $P(<ins class="diffchange diffchange-inline">D</ins>)$：</strong> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验前概率]]</strong>。在还没做检查前，这个病人患病的可能性有多大？这取决于<strong>流行病学数据</strong><del class="diffchange diffchange-inline">（如：该年龄段人群的患病率）。</del></span></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验前概率]]</strong>。在还没做检查前，这个病人患病的可能性有多大？这取决于<strong>流行病学数据</strong><ins class="diffchange diffchange-inline">（如：该年龄段人群的基础患病率）。</ins></span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px;"></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom<ins class="diffchange diffchange-inline">: 15px; border-left: 4px solid #b91c1c; padding-left</ins>: 15px;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #b91c1c;">2. 似然度 $P(<del class="diffchange diffchange-inline">\text{症状}</del>|<del class="diffchange diffchange-inline">\text{病}</del>)$：</strong> </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #b91c1c;">2. 似然度 $P(<ins class="diffchange diffchange-inline">S</ins>|<ins class="diffchange diffchange-inline">D</ins>)$：</strong> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">如果病人真有这个病，出现这个症状（或检查阳性）的概率是多少？这对应于诊断试验的<strong>[[敏感度]]</strong>。</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">如果病人真有这个病，出现这个症状（或检查阳性）的概率是多少？这对应于诊断试验的<strong>[[敏感度]]</strong>。</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom: 15px;"></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <li style="margin-bottom<ins class="diffchange diffchange-inline">: 15px; border-left: 4px solid #0f172a; padding-left</ins>: 15px;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #0f172a;">3. 后验概率 $P(<del class="diffchange diffchange-inline">\text{病}</del>|<del class="diffchange diffchange-inline">\text{症状}</del>)$：</strong> </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <strong style="color: #0f172a;">3. 后验概率 $P(<ins class="diffchange diffchange-inline">D</ins>|<ins class="diffchange diffchange-inline">S</ins>)$：</strong> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验后概率]]</strong>。看到检查结果阳性后，病人真正患病的概率。这才是医生和 AI 最终要输出的结论。</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><span style="color: #475569;">即<strong>[[验后概率]]</strong>。看到检查结果阳性后，病人真正患病的概率。这才是医生和 AI 最终要输出的结论。</span></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l82" >第82行：</td>
<td colspan="2" class="diff-lineno">第82行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 15px 0; text-align: justify;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> 贝叶斯推理揭示了一个反直觉的医学现象：<strong><del class="diffchange diffchange-inline">如果一种病非常罕见（先验概率极低），即使检查手段非常准确（敏感度高），阳性结果也很有可能是误诊（假阳性）。</del></strong></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> 贝叶斯推理揭示了一个反直觉的医学现象：<strong><ins class="diffchange diffchange-inline">如果一种病非常罕见（先验概率 $P(D)$ 极低），即使检查手段非常准确（敏感度 $P(S|D)$ 高），阳性结果也很有可能是误诊（假阳性）。</ins></strong></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><strong>AI 医生的启示：</strong> 当“智慧医生”看到一个年轻人（低风险）出现某种症状时，它不应直接跳到罕见癌症的诊断，因为先验概率太低；除非有极强的证据（极高的似然比）来扭转这一判断。这是防止 AI 出现“大惊小怪”误诊的关键逻辑。</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <br><strong>AI 医生的启示：</strong> 当“智慧医生”看到一个年轻人（低风险）出现某种症状时，它不应直接跳到罕见癌症的诊断，因为先验概率太低；除非有极强的证据（极高的似然比）来扭转这一判断。这是防止 AI 出现“大惊小怪”误诊的关键逻辑。</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </p></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <h2 style="background: #f1f5f9; color: #0f172a; padding: 10px 18px; border-radius: 0 6px 6px 0; font-size: 1.25em; margin-top: 40px; border-left: 6px solid #0f172a; font-weight: bold;">在 AI 系统中的实现</h2></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <h2 style="background: #f1f5f9; color: #0f172a; padding: 10px 18px; border-radius: 0 6px 6px 0; font-size: 1.25em; margin-top: 40px; border-left: 6px solid #0f172a; font-weight: bold;">在 AI 系统中的实现</h2></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l98" >第98行：</td>
<td colspan="2" class="diff-lineno">第97行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.92em; line-height: 1.6; color: #1e293b; margin-top: 50px; border-top: 2px solid #0f172a; padding: 15px 25px; background-color: #f8fafc; border-radius: 0 0 10px 10px;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.92em; line-height: 1.6; color: #1e293b; margin-top: 50px; border-top: 2px solid #0f172a; padding: 15px 25px; background-color: #f8fafc; border-radius: 0 0 10px 10px;"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <span style="color: #0f172a; font-weight: bold; font-size: 1.05em; display: inline-block; margin-bottom: 15px;">关键参考文献</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <span style="color: #0f172a; font-weight: bold; font-size: 1.05em; display: inline-block; margin-bottom: 15px;">关键参考文献</span></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"> </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 12px 0; border-bottom: 1px solid #e2e8f0; padding-bottom: 10px;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <p style="margin: 12px 0; border-bottom: 1px solid #e2e8f0; padding-bottom: 10px;"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> [1] <strong>Sackett DL, et al. (1991).</strong> <em>Clinical Epidemiology: A Basic Science for Clinical Medicine.</em><br></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> [1] <strong>Sackett DL, et al. (1991).</strong> <em>Clinical Epidemiology: A Basic Science for Clinical Medicine.</em><br></div></td></tr>
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https://www.yiliao.com/index.php?title=%E8%B4%9D%E5%8F%B6%E6%96%AF%E6%8E%A8%E7%90%86&diff=312630&oldid=prev
2026年1月4日 (日) 00:59 77921020
2026-01-04T00:59:59Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">←上一版本</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2026年1月4日 (日) 00:59的版本</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17" >第17行：</td>
<td colspan="2" class="diff-lineno">第17行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="padding: 25px; text-align: center; background-color: #f8fafc;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="padding: 25px; text-align: center; background-color: #f8fafc;"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="display: inline-block; background: #ffffff; border: 1px solid #e2e8f0; border-radius: 12px; padding: 20px; box-shadow: 0 4px 10px rgba(0,0,0,0.04);"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="display: inline-block; background: #ffffff; border: 1px solid #e2e8f0; border-radius: 12px; padding: 20px; box-shadow: 0 4px 10px rgba(0,0,0,0.04);"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> [[Image:Bayes_Theorem_Icon.png|100px|概率更新]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> [[Image:Bayes_Theorem_Icon.png|100px|概率更新<ins class="diffchange diffchange-inline">|链接=Special:FilePath/Bayes_Theorem_Icon.png</ins>]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.8em; color: #64748b; margin-top: 12px; font-weight: 600;">临床诊断的数学本质</div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="font-size: 0.8em; color: #64748b; margin-top: 12px; font-weight: 600;">临床诊断的数学本质</div></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l54" >第54行：</td>
<td colspan="2" class="diff-lineno">第54行：</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="background-color: #f8fafc; padding: 20px; border-radius: 8px; border: 1px solid #e2e8f0; text-align: center; margin: 20px 0;"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <div style="background-color: #f8fafc; padding: 20px; border-radius: 8px; border: 1px solid #e2e8f0; text-align: center; margin: 20px 0;"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <del class="diffchange diffchange-inline">$$</del>P(<del class="diffchange diffchange-inline">\text{病}</del>|<del class="diffchange diffchange-inline">\text{症状}</del>) <del class="diffchange diffchange-inline">= \frac{</del>P(<del class="diffchange diffchange-inline">\text{症状}|\text{病}</del>) <del class="diffchange diffchange-inline">\times </del>P(<del class="diffchange diffchange-inline">\text{病}</del>)<del class="diffchange diffchange-inline">}{</del>P(<del class="diffchange diffchange-inline">\text{症状}</del>)<del class="diffchange diffchange-inline">}$$</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <ins class="diffchange diffchange-inline">(敏感度) (基础患病率)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins>P(<ins class="diffchange diffchange-inline">症状</ins>|<ins class="diffchange diffchange-inline">有病</ins>) <ins class="diffchange diffchange-inline"> × </ins>P(<ins class="diffchange diffchange-inline">有病</ins>)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins>P(<ins class="diffchange diffchange-inline">确诊率</ins>) <ins class="diffchange diffchange-inline"> = ----------------------------------</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins>P(<ins class="diffchange diffchange-inline">出现症状的总概率</ins>)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l95" >第95行：</td>
<td colspan="2" class="diff-lineno">第98行：</td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <span style="color: #0f172a; font-weight: bold; font-size: 1.05em; display: inline-block; margin-bottom: 15px;">关键参考文献</span></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <span style="color: #0f172a; font-weight: bold; font-size: 1.05em; display: inline-block; margin-bottom: 15px;">关键参考文献</span></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> [1] <strong>Sackett DL, et al. (1991).</strong> <em>Clinical Epidemiology: A Basic Science for Clinical Medicine.</em><br></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> [1] <strong>Sackett DL, et al. (1991).</strong> <em>Clinical Epidemiology: A Basic Science for Clinical Medicine.</em><br></div></td></tr>
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https://www.yiliao.com/index.php?title=%E8%B4%9D%E5%8F%B6%E6%96%AF%E6%8E%A8%E7%90%86&diff=312628&oldid=prev
77921020：建立内容为“<div style="padding: 0 4%; line-height: 1.8; color: #1e293b; font-family: 'Helvetica Neue', Helvetica, 'PingFang SC', Arial, sans-serif; background-color: #ffffff…”的新页面
2026-01-04T00:57:21Z
<p>建立内容为“<div style="padding: 0 4%; line-height: 1.8; color: #1e293b; font-family: 'Helvetica Neue', Helvetica, 'PingFang SC', Arial, sans-serif; background-color: #ffffff…”的新页面</p>
<p><b>新页面</b></p><div><div style="padding: 0 4%; line-height: 1.8; color: #1e293b; font-family: 'Helvetica Neue', Helvetica, 'PingFang SC', Arial, sans-serif; background-color: #ffffff; max-width: 1200px; margin: auto;"><br />
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<strong>Bayesian Inference</strong>（<strong>贝叶斯推理</strong>）是一种基于概率统计的逻辑推理方法，其核心思想是：随着新证据（Evidence）的出现，不断更新对某一假设（Hypothesis）的置信度。在医学领域，贝叶斯推理是<strong>[[临床诊断]]</strong>的底层逻辑：医生并不是根据一个症状直接判定疾病，而是基于患者的<strong>[[验前概率]]</strong>（Pre-test Probability，如流行病学数据），结合检查结果的<strong>[[似然比]]</strong>（Likelihood Ratio），计算出患者患病的<strong>[[验后概率]]</strong>（Post-test Probability）。对于 AI 医生而言，贝叶斯网络是处理医疗<strong>不确定性</strong>和复杂因果关系的最有效数学模型。<br />
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<div style="font-size: 1.2em; font-weight: bold; letter-spacing: 1.2px;">Bayesian Inference</div><br />
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[[Image:Bayes_Theorem_Icon.png|100px|概率更新]]<br />
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<div style="font-size: 0.8em; color: #64748b; margin-top: 12px; font-weight: 600;">临床诊断的数学本质</div><br />
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<td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #0f172a;">$$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$</td><br />
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<th style="text-align: left; padding: 6px 12px; background-color: #f1f5f9; color: #475569; border-bottom: 1px solid #e2e8f0;">关键要素</th><br />
<td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #1e40af;">[[先验概率]], [[似然函数]], [[后验概率]]</td><br />
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<th style="text-align: left; padding: 6px 12px; background-color: #f1f5f9; color: #475569; border-bottom: 1px solid #e2e8f0;">应用领域</th><br />
<td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #0f172a;">CDSS, 基因诊断, 垃圾邮件过滤</td><br />
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<td style="padding: 6px 12px; border-bottom: 1px solid #e2e8f0; color: #0f172a;">[[贝叶斯网络]] (Bayesian Networks)</td><br />
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<th style="text-align: left; padding: 6px 12px; background-color: #f1f5f9; color: #475569;">核心标签</th><br />
<td style="padding: 6px 12px; color: #1e40af;">[[诊断逻辑]], [[不确定性]]</td><br />
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贝叶斯公式是所有医生潜意识里都在使用的工具，哪怕他们自己没有意识到：<br />
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$$P(\text{病}|\text{症状}) = \frac{P(\text{症状}|\text{病}) \times P(\text{病})}{P(\text{症状})}$$<br />
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<strong style="color: #1e40af;">1. 先验概率 $P(\text{病})$：</strong> <br />
<br><span style="color: #475569;">即<strong>[[验前概率]]</strong>。在还没做检查前，这个病人患病的可能性有多大？这取决于<strong>流行病学数据</strong>（如：该年龄段人群的患病率）。</span><br />
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<strong style="color: #b91c1c;">2. 似然度 $P(\text{症状}|\text{病})$：</strong> <br />
<br><span style="color: #475569;">如果病人真有这个病，出现这个症状（或检查阳性）的概率是多少？这对应于诊断试验的<strong>[[敏感度]]</strong>。</span><br />
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<strong style="color: #0f172a;">3. 后验概率 $P(\text{病}|\text{症状})$：</strong> <br />
<br><span style="color: #475569;">即<strong>[[验后概率]]</strong>。看到检查结果阳性后，病人真正患病的概率。这才是医生和 AI 最终要输出的结论。</span><br />
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<h2 style="background: #f1f5f9; color: #0f172a; padding: 10px 18px; border-radius: 0 6px 6px 0; font-size: 1.25em; margin-top: 40px; border-left: 6px solid #0f172a; font-weight: bold;">临床应用场景：为什么“基线”很重要</h2><br />
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贝叶斯推理揭示了一个反直觉的医学现象：<strong>如果一种病非常罕见（先验概率极低），即使检查手段非常准确（敏感度高），阳性结果也很有可能是误诊（假阳性）。</strong><br />
<br><strong>AI 医生的启示：</strong> 当“智慧医生”看到一个年轻人（低风险）出现某种症状时，它不应直接跳到罕见癌症的诊断，因为先验概率太低；除非有极强的证据（极高的似然比）来扭转这一判断。这是防止 AI 出现“大惊小怪”误诊的关键逻辑。<br />
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<h3 style="margin-top: 0; color: #1e40af; font-size: 1.1em; border-bottom: 1px solid #e2e8f0; padding-bottom: 10px;">Bayesian Networks (贝叶斯网络)</h3><br />
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在构建 CDSS 时，我们通常将医学知识图谱转化为贝叶斯网络。图中的节点代表变量（如“吸烟”、“肺癌”、“咳嗽”），边代表因果依赖关系。AI 系统可以通过观察到的变量（如“咳嗽”=True），利用贝叶斯推理计算出未观察变量（如“肺癌”）的概率分布。<br />
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<span style="color: #0f172a; font-weight: bold; font-size: 1.05em; display: inline-block; margin-bottom: 15px;">关键参考文献</span><br />
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[1] <strong>Sackett DL, et al. (1991).</strong> <em>Clinical Epidemiology: A Basic Science for Clinical Medicine.</em><br><br />
<span style="color: #475569;">[基础]：经典教科书，详细阐述了如何利用贝叶斯诺模图（Fagan's Nomogram）在床旁快速进行概率转换。</span><br />
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[2] <strong>Pearl J. (1988).</strong> <em>Probabilistic Reasoning in Intelligent Systems.</em><br><br />
<span style="color: #475569;">[AI 奠基]：图灵奖得主 Judea Pearl 的著作，奠定了贝叶斯网络在人工智能推理中的核心地位，将因果推断引入了 AI。</span><br />
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贝叶斯推理 · 知识图谱<br />
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<td style="padding: 10px 15px; color: #334155;">[[概率论]] • [[人工智能逻辑]]</td><br />
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<td style="padding: 10px 15px; color: #334155;">[[先验概率]] (Prior) • [[似然比]] (LR) • [[敏感度与特异度]]</td><br />
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<td style="width: 85px; background-color: #f8fafc; color: #334155; font-weight: 600; padding: 10px 12px; text-align: right; vertical-align: middle; white-space: nowrap;">临床应用</td><br />
<td style="padding: 10px 15px; color: #334155;">[[Fagan诺模图]] • [[诊断试验评价]] • [[风险预测模型]]</td><br />
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<td style="width: 85px; background-color: #f8fafc; color: #334155; font-weight: 600; padding: 10px 12px; text-align: right; vertical-align: middle; white-space: nowrap;">对比概念</td><br />
<td style="padding: 10px 15px; color: #334155;">[[频率学派]] (Frequentist Inference)</td><br />
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