Binary Bayes Net Demo: C -> T

Conditional Probability Playground

Setup: a person either has the condition (C=1) or does not (C=0). The test can come back positive (T=1) or negative (T=0). The arrow C -> T means the true condition affects how likely each test result is.

P(C): Probability the condition is present (C = 1)

C	P(C)
0	0.990
1	0.010

Conditional P(T | C)

C	P(T=1\|C)	P(T=0\|C)
1	0.950	0.050
0	0.050	0.950

Scenario preset

Prior/base rate (chance condition is present) = P(C=1) 0.010

sensitivity = P(T=1 | C=1) 0.950

false positive rate = P(T=1 | C=0) 0.050

Show expected counts out of N 1000

Joint table P(C,T)

	T=0	T=1
C=0	0.941	0.050
C=1	0.001	0.010

Evidence and Posterior

Choose observed evidence for T. Posterior updates by Bayes' rule using the normalizer P(T).

Observed T = 1 (positive) Observed T = 0 (negative)

P(T=1) = 0.059

P(T=0) = 0.941

Posterior table P(C | T = observed)

C	P(C \| T=1)
0	0.839
1	0.161

How to read this:
Prior/base rate: starting chance before seeing test data, P(C).
Likelihood/CPT: test behavior given condition, P(T|C).
Evidence: pick observed T.
Posterior: updated belief P(C|T) = (prior x likelihood) / P(T).