Mathematical Methods for Physics and Engineering - Matematica.NET

STATISTICSThus, a Bayesian statistician considers the ML estimates â ML of the parametersto be the values that maximise the posterior P (a|x,H) under the assumption ofa uniform prior. More importantly, however, a Bayesian would not calculate thestandard error or confidence interval on this estimate using the (classical) methodemployed in subsection 31.3.4. Instead, a far more straightforward approach isadopted. Let us assume, for the moment, that one is estimating just a singleparameter a. Using (31.83), we may determine the values a − and a + such thatPr(a a + |x,H)= L(x; a) da = β.a +where∫it is assumed that the likelihood has been normalised in such a way thatL(x; a) da = 1. Combining these equations gives∫ a+Pr(a − ≤ a