Bayes' Theorem

$P(B|A)=\frac{P(A|B)P(B)}{P(A)}=\frac{P(A\cap B)}{P(B)}$

• $P(A)$ may be substituted using Law of Total Probability

$P(D+|T+)=\frac{P(T+|D+)P(D+)}{P(T+|D+)P(D+)+P(T+|D-)P(D-)}$

• Positive predictive value of a diagnostic test given test sensitivity, test specificity, and proportion of sick/healthy people in a population

$P(\theta |x)=\frac{P(x|\theta )P(\theta )}{P(x)}$

• $P(\theta |x)$ is the posterior
• $P(x|\theta )$ is the likelihood
• $P(\theta )$ is the prior
• $P(x)$ is the marginal