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
COMPLETING YOUR FIRST BAYESIAN COMPUTATIONS
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
Illustration 2: Adverse Event Rates
Conclusions
BAYESIAN SAMPLE SIZE
Introduction
The Real Purpose of Sample Size Discussions
Hybrid Bayesian-Frequentist Sample Sizes
Complete Bayesian Sample Size Computations
Conclusions
Problems
PREDICTIVE POWER AND ADAPTIVE PROCEDURES
Introduction
Predictive Power
Adaptive Bayes Procedures
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.
Biography
Moyé, Lemuel A.
"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
