3.7 Coursera Notes Inference
Bayesian inference updates prior beliefs with accumulated evidence. The posterior odds equals the prior odds multiplied by the likelihood ratio of observing evidence under the competing hypotheses.
\[\frac{P(H1|D)}{P(H0|D)} = \frac{P(D|H1)}{P(D|H0)} \times \frac{P(H1)}{P(H0)}\]
(*This isn’t quite what I expected. Wouldn’t you replace the likelihood ratio, \(\frac{P(D|H1)}{P(D|H0)}\) with the proportional adjustment, \(\frac{P(D|H1)}{P(D)}\)?)
Express the prior