Elementary Bayesian Biostatistics

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 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.