Bayesian Statistic Approach
Bayes' Theorem
Conditional Probability
Parameters can be updated by new information p(A)
Bayesian Paradigm
p(A|B) = {p(B|A)p(A)} /p(B)
f(θ|x) ∝ f(x|θ) f(θ)
θ : parameter being estimated (unknown)
f(x) : normalizing constant ( has been left out )
x : represent the data
f(x|θ) : likelihood function relating the data x and (unknown) parameter θ
f(θ) : prior (can be updated by new information)
same as Conjugate Prior
has no information about θ
f(θ|x) : posterior distribution
to make predictions for unknown data
sample from it to get the distribution of parameter θ
to estimate the unknown parameter θ (Credible Interval)
We know something
We know very little
Proper (Informative) Prior
Uninformative prior - Beta(1,1)
Improper prior - Beta(0,0)
Conjugate Prior
Type of Posterior = Type of Prior