• prior beliefs are taken about various possibles, leading to the assumption of a prior distribution for the parameter of interest;
• these are then modified by a likelihood function derived from the data collected, to arrive at posterior beliefs, or a posterior distribution:

p(q|x) = f(x|q) p(q) / ò f(x|q ) p(q) dq

• Posterior = Prior ´ Likelihood

Rearranging the terms in the first equation yields an expression for P(q|x), or the posterior probability of obtaining the parameter q given the data at hand :

P(q|x) = P(x|q) P(q) / P(x)

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