Concept - Bayes Rule

Statement (s.13): by definition of conditional probability, $p(h|D)=\frac{p(h,D)}{p(D)}=\frac{p(D|h)p(h)}{p(D)}$ Also called “Reverse Probability” (s.13).

Term	Name (s.13)
$P(h)$	prior probability of hypothesis $h$ (Concept - Prior Probability)
$P(h	D)$
$P(D	h)$
$P(D)$	prior probability of evidence $D$

Example (s.14), H6751 student model: $P(\text{library}|H6751)=0.8$, $P(H6751)=1/100$, $P(\text{library})=1/10$; question: $p(h|D)$ for a student who stays in the library? Slide leaves it blank.

Added context

$p(h|D)=0.8\times 0.01/0.1=0.08$.

Evolution of posteriors (s.15-17): starting from a flat prior, each new piece of data ($D1$, then $D2$) concentrates probability mass on fewer hypotheses (bar chart gets narrower and taller).

Leads to Concept - Maximum A Posteriori and to Concept - Naive Bayes.

Related

Concept - Conditional Probability, Concept - Maximum A Posteriori, Concept - Maximum Likelihood Estimation

Source: 03 Text Classification - Chunk 01 (s.1-30)