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# Elementary Bayesian Biostatistics

By

## Lemuel A. Moyé

ISBN 9780367388799
Published October 18, 2019 by Chapman and Hall/CRC
400 Pages 123 B/W Illustrations

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## Book Description

Bayesian analyses have made important inroads in modern clinical research due, in part, to the incorporation of the traditional tools of noninformative priors as well as the modern innovations of adaptive randomization and predictive power. Presenting an introductory perspective to modern Bayesian procedures, Elementary Bayesian Biostatistics explores Bayesian principles and illustrates their application to healthcare research.

Building on the basics of classic biostatistics and algebra, this easy-to-read book provides a clear overview of the subject. It focuses on the history and mathematical foundation of Bayesian procedures, before discussing their implementation in healthcare research from first principles. The author also elaborates on the current controversies between Bayesian and frequentist biostatisticians. The book concludes with recommendations for Bayesians to improve their standing in the clinical trials community. Calculus derivations are relegated to the appendices so as not to overly complicate the main text.

As Bayesian methods gain more acceptance in healthcare, it is necessary for clinical scientists to understand Bayesian principles. Applying Bayesian analyses to modern healthcare research issues, this lucid introduction helps readers make the correct choices in the development of clinical research programs.

PREFACE
INTRODUCTION

PROLOGUE: OPENING SALVOS

BASIC PROBABILITY AND BAYES THEOREM
Probability's Role
Objective and Subjective Probability
Relative Frequency and Collections of Events
Counting and Combinatorics
Simple Rules in Probability
Law of Total Probability and Bayes Theroem

COMPOUNDING AND THE LAW OF TOTAL PROBABILITY
Introduction
The Law of Total Probability: Compounding
Proportions and the Binomial Distribution
Negative Binomial Distribution
The Poisson Process
The Uniform Distribution
Exponential Distribution
Problems

INTERMEDIATE COMPOUNDING AND PRIOR DISTRIBUTIONS
Compounding and Prior Distributions
The Force of Effect Size
Epidemiology 101
Computing Distributions of Deaths
The Gamma Distribution and ER Arrivals
The Normal Distribution
Problems

Compounding and Bayes Procedures
Introduction to a Simple Bayes Procedure
Including a Continuous Conditional Distribution
Working with Continuous Conditional Distributions
Continuous Conditional and Prior Distributions
Problems

WHEN WORLDS COLLIDE
Introduction

DEVELOPING PRIOR PROBABILITY
Introduction
Prior Knowledge and Subjective Belief
The Counterintuitive Prior
Prior Information from Different Investigators
Meta Analysis and Prior Distributions
Priors and Clinical Trials
Conclusions
Problems

USING POSTERIOR DISTRIBUTIONS: LOSS AND RISK
Introduction
The Role of Loss and Risk
Decision Theory Dichotomous Loss
Generalized Discrete Loss Functions
Continuous Loss Functions
The Need for Realistic Loss Functions
Problems

PUTTING IT ALL TOGETHER
Introduction
Illustration 1: Stroke Treatment
Conclusions

BAYESIAN SAMPLE SIZE
Introduction
The Real Purpose of Sample Size Discussions
Hybrid Bayesian-Frequentist Sample Sizes
Complete Bayesian Sample Size Computations
Conclusions
Problems

Introduction
Predictive Power
Conclusions

IS MY PROBLEM A BAYES PROBLEM?
Introduction
Unidimensional versus Multidimensional Problems
Ovulation Timing
Building Community Intuition

CONCLUSIONS AND COMMENTARY
Validity of the Key Ingredients
Dark Clouds
Recommendations

APPENDICES
Compound Poisson Distribution
Evaluations Using the Uniform Distribution
Computations for the Binomial-Uniform Distribution
Binomial-Exponential Compound Distribution
Poisson-Gamma Processes
Gamma and Negative Binomial Distribution
Gamma Compounding with Gamma Distribution
Standard Normal Distribution
Compound and Conjugate Normal Distributions
Uniform Prior and Conditional Normal Distribution
Beta Distribution
Calculations for Chapter 8
Sample Size Primer
Predictive Power Computations

INDEX

References appear at the end of each chapter.

...

Moyé, Lemuel A.

## Reviews

"This is a fun book for teaching oneself (or others) both some fundamental principles of epidemiology and clinical trials and fundamental principles of probability and statistical inference from the point of view of a practising clinical scientist who is also a very knowledgeable, no-nonsense Bayesian. What makes it very different from common textbooks is its blending of history, controversy (about probability, statistics, and clinical studies), real-life examples, and wise practical advice. … a very readable introduction to basic probability models, inference questions, and Bayesian answers without calculus and Markov chain Monte Carlo. …"
International Statistical Review, 2008

". . . provides a very clear exposition of Bayesian thinking for applications in biostatistics. The book’s strengths lie in its careful discussions of Bayesian thinking or problems in health care research, including the constructions of priors and loss functions . . . a welcome addition to the growing number of books that describe Bayesian modeling from an applied perspective."

–Jim Albert, Bowling Green State University, in JASA, December 2008