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Basic Principles of Bayesian Statistical Inference - December 13, 2016

Basic Principles of Bayesian Statistical Inference

M. Reza Meshkani

Department of Statistics, Shahid Beheshti University

Monday, December 13, 2016, 12:30 -13:30

University of Tehran

School of Mathematics, Statistics and Computer Science

Hashtroodi hall

Abstract: In this talk, first an outline of a scientific research process is explained. This is used to motivate the necessity of statistical analyses in scientific research by formulating the problem, designing the study, gathering the data, analyzing the data, and interpreting the results.

Second, the major roles of statistics in achieving the above goals in the framework of data reduction, data analysis, and reaching to desired inferences are discussed. Based on these preliminaries, we argue in favor of Bayesian statistical inference and its methods in data analyses.

Third, we review the basic principles of Bayesian statistical inference reviewing its major elements. Principles of sufficiency, likelihood, and conditionality are explained and their observation in Frequentist and Bayesian Inference are discussed. Existence of utility and prior are reviewed. Posterior analysis is discussed.

Fourth, an example is given which illustrates the theoretical material given in the talk by providing methods for estimation, hypothesis testing, and prediction of the parameter of interest.