A comparison of the bayesian and frequentist approaches to estimation

This monograph contributes to the area of comparative statistical inference. Attention is restricted to the important subfield of statistical estimation. The book is intended for an audience having a solid grounding in probability and statistics at the level of the year-long undergraduate course taken by statistics and mathematics majors. The necessary background on Decision Theory and the frequentist and Bayesian approaches to estimation is presented and carefully discussed in Chapters 1–3. The “threshold problem” - identifying the boundary between Bayes estimators which tend to outperform standard frequentist estimators and Bayes estimators which don’t - is formulated in an analytically tractable way in Chapter 4. The formulation includes a specific (decision-theory based) criterion for comparing estimators. The centerpiece of the monograph isChapter 5 in which, under quite general conditions, an explicit solution to the threshold is obtained for the problem of estimating a scalar parameter under squared error loss. The six chapters that follow address a variety of other contexts in which the threshold problem can be productively treated. Included are treatments of the Bayesian consensus problem, the threshold problem for estimation problems involving of multi-dimensional parameters and/or asymmetric loss, the estimation of nonidentifiable parameters, empirical Bayes methods for combining data from ‘similar’ experiments and linear Bayes methods for combining data from ‘related’ experiments. The final chapter provides an overview of the monograph’s highlights and a discussion of areas and problems in need offurther research. An excellent introduction to Bayesian theory and methods, while taking an impartial view of their merits relative to the alternative 'classical' or 'frequentist' approach A very readable presentation of the basic characteristics of statistical inference from a Bayesian and from a frequentist perspective Offers a resolution of one of the most intense scientific debates in the past 250 years INDICE: Point estimation from a decision theoretic viewpoint.- An overviewof the frequentist approach to estimation.- An overview of the Bayesian approach to estimation.- The threshold problem.- Comparing Bayesian and frequentistestimators of a scalar parameter.- Conjugacy, self consistency, and Bayesian consensus.- Bayesian vs. frequentist shrinkage in multivariate normal problems.- Comparing Bayesian and frequentist estimators under asymmetric loss.- The treatment of nonidentifiable models.- Improving on standard Bayesian and frequentist estimators.- Combining data from 'related' experiments.- Fatherly advice.

• ISBN: 978-1-4419-5940-9
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 226
• Fecha Publicación: 01/07/2010
• Nº Volúmenes: 1
• Idioma: Inglés