Statistical Modelling By Exponential Families
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Statistical Modelling by Exponential Families
Author: Rolf Sundberg
language: en
Publisher: Cambridge University Press
Release Date: 2019-08-29
A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.
Exponential Families of Stochastic Processes
Author: Uwe Küchler
language: en
Publisher: Springer Science & Business Media
Release Date: 1997-07-10
A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.
Graphical Models, Exponential Families, and Variational Inference
The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.