In defining Bayesian statistics as a system of describing epistemology uncertainty using mathematical language of probability. In the theorem degree of believes in state of nature are specified ,non-negative. The method :
start with existing 'Prior' beliefs.
Update these beleives using data to give 'posterior' beliefs.
and these may be used as basis for inferential decision.
The theory result in conditional probability and stating that:
For two quantities( y and x ), y represent data, and x represent parameters.
P(x/y) = p(y/x) p(x)/ p(y) , where :
p(0) denote probability distribution and p(0/0) conditional distribution.
The prior distribution p(x) is combined with p(y/x) to provide a posterior distribution.
How would you describe the difference between Bayesian approach and Bayes' Rule? Why would you choose one over the other in a statistical approach?