Medical Diagnosis

Problem 3.5 • Given symptoms, which disease is most likely? (Multiple diseases)

🏥 Diseases & Prevalence

🦠
Disease A
Prevalence 1.0%
P(S₁|A) 90%
P(S₂|A) 70%
🧬
Disease B
Prevalence 0.5%
P(S₁|B) 60%
P(S₂|B) 95%
💊
Disease C
Prevalence 2.0%
P(S₁|C) 40%
P(S₂|C) 30%

🩺 Observed Symptoms

📊 Posterior Probabilities

Disease A
0%
Disease B
0%
Disease C
0%
Most Likely Diagnosis
Disease A
75.2% confidence

⚙️ Adjust Parameters

Disease A

Prevalence1.0%

Disease B

Prevalence0.5%

Disease C

Prevalence2.0%

📐 Bayes for Multiple Hypotheses

P(Dᵢ|S₁,S₂) ∝
P(S₁|Dᵢ)·P(S₂|Dᵢ)·P(Dᵢ)

Assuming symptoms are conditionally independent given disease.