Bayesian inference is different from classical inference, in that one is concerned with answering the following question, ``What should a rational person believe, after collecting the data, and given what was believed before the data was collected?''
Essentially, this question differs from what a classical statistician asks in a number of different ways;
The Bayesian framework has attractions for a number of reasons [5]. Bayesian statistics has a strong axiomatic foundation, it incorporates prior information directly into the analysis, and it has a naturally formulated decision structure. Bayesian inference has not been as commonly used as frequentist methods in the past, in part due to computational complexities [27]. Since about 1960 there has been a revival of interest [38] to the extent that it is now well established as an alternative to classical methods.
As to the question of why one might choose to undertake a Bayesian analysis of a situation, rather than an appropriate classical analysis, the answer is simple. Apart from the philosophical reasons, for a number of real problems the answer is that the methodology works [46] .
