Christensen / Johnson / Branscum Bayesian Ideas and Data Analysis

An Introduction for Scientists and Statisticians
1. Auflage 2013
ISBN: 978-1-4398-9151-3
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 516 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

Emphasizing the use of WinBUGS and R to analyze real data, Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians presents statistical tools to address scientific questions. It highlights foundational issues in statistics, the importance of making accurate predictions, and the need for scientists and statisticians to collaborate in analyzing data. The WinBUGS code provided offers a convenient platform to model and analyze a wide range of data.

The first five chapters of the book contain core material that spans basic Bayesian ideas, calculations, and inference, including modeling one and two sample data from traditional sampling models. The text then covers Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) simulation. After discussing linear structures in regression, it presents binomial regression, normal regression, analysis of variance, and Poisson regression, before extending these methods to handle correlated data. The authors also examine survival analysis and binary diagnostic testing. A complementary chapter on diagnostic testing for continuous outcomes is available on the book’s website. The last chapter on nonparametric inference explores density estimation and flexible regression modeling of mean functions.

The appropriate statistical analysis of data involves a collaborative effort between scientists and statisticians. Exemplifying this approach, Bayesian Ideas and Data Analysis focuses on the necessary tools and concepts for modeling and analyzing scientific data.

Data sets and codes are provided on a supplemental website.

Zielgruppe

Advanced undergraduate and graduate students in statistics, biostatistics, epidemiology, and science; statisticians; professionals in science and engineering.

Autoren/Hrsg.

Christensen, Ronald

Johnson, Wesley O.

Branscum, Adam J.

Hanson, Timothy E.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Prologue

Probability of a Defective: Binomial Data

Brass Alloy Zinc Content: Normal Data

Armadillo Hunting: Poisson Data

Abortion in Dairy Cattle: Survival Data

Ache Hunting with Age Trends

Lung Cancer Treatment: Log-Normal Regression

Survival with Random Effects: Ache Hunting

Fundamental Ideas I

Simple Probability Computations

Science, Priors, and Prediction

Statistical Models

Posterior Analysis

Commonly Used Distributions

Integration versus Simulation

Introduction

WinBUGS I: Getting Started

Method of Composition

Monte Carlo Integration
Posterior Computations in R

Fundamental Ideas II
Statistical Testing
Exchangeability

Likelihood Functions

Sufficient Statistics

Analysis Using Predictive Distributions

Flat Priors

Jeffreys’ Priors

Bayes Factors
Other Model Selection Criteria
Normal Approximations to Posteriors
Bayesian Consistency and Inconsistency

Hierarchical Models

Some Final Comments on Likelihoods
Identifiability and Noninformative Data

Comparing Populations

Inference for Proportions
Inference for Normal Populations
Inference for Rates
Sample Size Determination
Illustrations: Foundry Data

Medfly Data

Radiological Contrast Data

Reyes Syndrome Data
Corrosion Data
Diasorin Data
Ache Hunting Data
Breast Cancer Data

Simulations

Generating Random Samples

Traditional Monte Carlo Methods
Basics of Markov Chain Theory
Markov Chain Monte Carlo

Basic Concepts of Regression
Introduction

Data Notation and Format

Predictive Models: An Overview

Modeling with Linear Structures
Illustration: FEV Data

Binomial Regression
The Sampling Model

Binomial Regression Analysis
Model Checking
Prior Distributions
Mixed Models
Illustrations: Space Shuttle Data

Trauma Data
Onychomycosis Fungis Data
Cow Abortion Data

Linear Regression
The Sampling Model

Reference Priors
Conjugate Priors

Independence Priors

ANOVA
Model Diagnostics

Model Selection
Nonlinear Regression
Illustrations: FEV Data

Bank Salary Data
Diasorin Data
Coleman Report Data
Dugong Growth Data

Correlated Data

Introduction

Mixed Models

Multivariate Normal Models

Multivariate Normal Regression

Posterior Sampling and Missing Data
Illustrations: Interleukin Data

Sleeping Dog Data
Meta-Analysis Data
Dental Data

Count Data

Poisson Regression
Over-Dispersion and Mixtures of Poissons
Longitudinal Data
Illustrations: Ache Hunting Data

Textile Faults Data
Coronary Heart Disease Data
Foot and Mouth Disease Data

Time to Event Data
Introduction
One-Sample Models
Two-Sample Data
Plotting Survival and Hazard Functions
Illustrations: Leukemia Cancer Data

Breast Cancer Data

Time to Event Regression

Accelerated Failure Time Models
Proportional Hazards Modeling
Survival with Random Effects
Illustrations: Leukemia Cancer Data

Larynx Cancer Data
Cow Abortion Data
Kidney Transplant Data
Lung Cancer Data
Ache Hunting Data

Binary Diagnostic Tests

Basic Ideas

One Test, One Population

Two Tests, Two Populations

Prevalence Distributions
Illustrations: Coronary Artery Disease

Paratuberculosis Data
Nucleospora Salmonis Data
Ovine Progressive Pnemonia Data

Nonparametric Models
Flexible Density Shapes
Flexible Regression Functions

Proportional Hazards Modeling
Illustrations: Galaxy Data

ELISA Data for Johnes Disease
Fungus Data
Test Engine Data
Lung Cancer Data

Appendix A: Matrices and Vectors
Appendix B: Probability
Appendix C: Getting Started in R
References

Über Autor(innen)

Ronald Christensen is a Professor in the Department of Mathematics and Statistics at the University of New Mexico, Albuquerque. He is also a Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics as well as the former Chair of the ASA Section on Bayesian Statistical Science.
Wesley Johnson is a Professor in the Department of Statistics at the University of California, Irvine. He is also a Fellow of the ASA and Chair-Elect of the ASA Section on Bayesian Statistical Science.
Adam Branscum is an Associate Professor in the Department of Public Health at Oregon State University, Corvallis.
Timothy E. Hanson is an Associate Professor in the Department of Statistics at the University of South Carolina, Columbia.