Bayesian Posterior

• When D is fixed though, this becomes a function of Model Candidates
• Non negative on K dim param space
• Not a PDF but if we divide it by its integral → PDF .
  • $\frac{p_{{\otimes }_i}x(D|\theta )h(\theta )}{{\int }_{{\mathbb{R}}^K}{p}_{{\otimes }_i}x(D|\theta )h(\theta )d\theta }$
  • Prob distrib over candidate models
• If the denominator is replaced written as $p(D)$ then it looks like the Bayes Rule
• Shape : $P(D|\theta )h(\theta )$
  • Integral not 1
  • Proto Distributions on $\theta$ space