#P03 · 概率统计与AI优化 (Probability & AI) · Lv.3在3D思维导图中查看

贝叶斯定理 (后验概率推断)

Thomas Bayes & Pierre-Simon Laplace · 1763년

P(H \mid E) = \frac{P(E \mid H)P(H)}{P(E)} = \frac{P(E \mid H)P(H)}{P(E\mid H)P(H)+P(E\mid H^c)P(H^c)}

\text{Posterior} \propto \text{Likelihood} \times \text{Prior}

结合先验概率 P(H) 与新证据 E 的似然度 P(E|H) 来更新后验概率 P(H|E)，是统计推断与AI不确定性推理的核心定律。

🧮 即时公式计算器与图形绘制器

先验概率 P(H)

灵敏度 P(E|H)

假阳性率 P(E|Hᶜ)

P(H\mid E) = \frac{0.95\times 0.05}{0.1425} = 33.33\%

사후확률 P(H|E)

33.33%

2차 연속 양성 시 사후확률

82.61%

전체 양성률 P(E)

14.25%

先修概念路径 (Prerequisite Path) (5 STEP)

按顺序点击即可沿3D霓虹路径从基础直达目标公式。

ax + b = 0 \implies x = -\frac{b}{a}

(a+b)^2 = a^2 + 2ab + b^2

{}_nP_r = \frac{n!}{(n-r)!}

P(A \mid B) = \frac{P(A \cap B)}{P(B)}

P(H \mid E) = \frac{P(E \mid H)P(H)}{P(E)} = \frac{P(E \mid H)P(H)}{P(E\mid H)P(H)+P(E\mid H^c)P(H^c)}

'원인→결과' 확률 P(증상|질병)만 알고 있을 때, 거꾸로 '결과→원인' 확률 P(질병|증상)을 희귀도(사전확률)까지 반영해 정확히 뒤집어 줍니다.

直接驱动垃圾邮件过滤(朴素贝叶斯)、医疗AI诊断校准、自动驾驶卡尔曼/粒子滤波及贝叶斯超参数优化。

#Spam Filter#Bayesian Inference#Medical AI Diagnosis#Kalman Filter

const bayes = (prior, sens, fpr) => (sens * prior) / (sens * prior + fpr * (1 - prior));