Posterior Distribution

Gist

Using the Bayes formula we know that:

P r (A | B) = Pr (B | A) Pr (A)

which for our observed data $y$ and model parameter $θ$ can be rewritten as:

P r (θ | y) = P r (y | θ) P r (θ) $ $ H o w e v e r, a n a l y t i c a l e x p r e s s i o n s a r e i m p o s s i b l e a l o t o f t i m e s s o w e n e e d t o b e a b l e t o s i m u l a t e f r o m t h e p o s t e r i o r d i s t r i b u t i o n t h r o u g h m e t h o d s l i k e [[T e c h n i c a l C o n c e p t s / B a y e s i a n / M a r k o v C h a i n M o n t e C a r l o ∥ M a r k o v C h a i n M o n t e C a r l o]] .