From Statistical Physics to Statistical Inference And Back

This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features.

Unlock the Power of Statistical Analysis to Uncover Relationships and Make Informed Decisions

In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory.

Authors: Brombin, C., Salmaso, L., Fontanella, L., Ippoliti, L., Fusilli, C.
Explores specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric testsUses the Expectation Maximization (EM) algorithm to give essential results for a likelihood-based approach to statistical inference in shape analysisCovers the theory of NonParametric Combination (NPC) tests as well as the applications of the methodology to the Face and Gesture Recognition Research Network (FG-NET) data