Procrustean statistical inference of deformations

Review of the Applications of Exponential Family in Statistical Inference

‎In this paper‎, ‎after introducing exponential family and a history of work done by researchers in the field of statistics‎, ‎some applications of this family in statistical inference especially in estimation problem‎,‎statistical hypothesis testing and statistical information theory concepts will be discussed‎.

Statistical Methodology for Deformations

Statistical Inference

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...

Statistical Inference

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 ...

Statistical Inference

Statistical Inference and Statistical Mechanics

In this lecture, recent developments on connections between Markov processes and nonequilibrium statistical mechanical systems are discussed. A statistical mechanical analogy is developed for Markov processes and a local entropic measure of their true asymmetry is defined. Introducing partial observations, conditional and joint analogies are developed for Markov processes and their optimal filt...