At the heart of statistics lie the ideas of statistical inference. Methods of statistical inference enable the investigator to argue from the particular observations in a sample to the general case. In contrast to logical deductions made from the general case to the specific case, a statistical inference can sometimes be incorrect. Nevertheless, one of the great intellectual advances of the twe...

λn = f1(x1)f1(x2) · · · f1(xn) f0(x1)f0(x2) · · · f0(xn) where we have simplified the notation by writing f0(x) for f(x | θ0) and f1(x) for f(x | θ1). A Likelihoodist Statistician would find the likelihood ratio λn to be the best direct measure of the relative support of the data for these two hypotheses; a Bayesian statistician with prior probabilities π0 = P[H0] and π1 = P[H1] = (1−π0) would ...