Applied Stochastic Modelling (Paperback, 2)

Introduction and Examples

Introduction

Examples of data sets

Basic Model Fitting

Introduction

Maximum-likelihood estimation for a geometric model

Maximum-likelihood for the beta-geometric model

Modelling polyspermy

Which model?

What is a model for?

Mechanistic models

Function Optimisation

Introduction

MATLAB: graphs and finite differences

Deterministic search methods

Stochastic search methods

Accuracy and a hybrid approach

Basic Likelihood Tools

Introduction

Estimating standard errors and correlations

Looking at surfaces: profile log-likelihoods

Confidence regions from profiles

Hypothesis testing in model selection

Score and Wald tests

Classical goodness of fit

Model selection bias

General Principles

Introduction

Parameterisation

Parameter redundancy

Boundary estimates

Regression and influence

The EM algorithm

Alternative methods of model fitting

Non-regular problems

Simulation Techniques

Introduction

Simulating random variables

Integral estimation

Verification

Monte Carlo inference

Estimating sampling distributions

Bootstrap

Monte Carlo testing

Bayesian Methods and MCMC

Basic Bayes

Three academic examples

The Gibbs sampler

The Metropolis?Hastings algorithm

A hybrid approach

The data augmentation algorithm

Model probabilities

Model averaging

Reversible jump MCMC (RJMCMC)

General Families of Models

Common structure

Generalised linear models (GLMs)

Generalised linear mixed models (GLMMs)

Generalised additive models (GAMs)

Index of Data Sets

Index of MATLAB Programs

Appendix A: Probability and Statistics Reference
Appendix B: Computing
Appendix C: Kernel Density Estimation

Solutions and Comments for Selected Exercises

Bibliography

Index

Discussions and Exercises appear at the end of each chapter.