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.
Biography
Byron J.T. Morgan
Praise for the First Edition
The author’s enthusiasm for his subject shines through this book. There are plenty of interesting example data sets … The book covers much ground in quite a short space … In conclusion, I like this book and strongly recommend it. It covers many of my favourite topics. In another life, I would have liked to have written it, but Professor Morgan has made a better job if it than I would have done.
—Tim Auton, Journal of the Royal Statistical SocietyI am seriously considering adopting Applied Stochastic Modelling for a graduate course in statistical computation that our department is offering next term.
—Jim Albert, Journal of the American Statistical Association…very well written, fresh in its style, with lots of wonderful examples and problems.
—R.P. Dolrow, TechnometricsA useful tool for both applied statisticians and stochastic model users of other fields, such as biologists, sociologists, geologists, and economists.
—Zentralblatt MATHThe book is a delight to read, reflecting the author’s enthusiasm for the subject and his wide experience. The layout and presentation of material are excellent. Both for new research students and for experienced researchers needing to update their skills, this is an excellent text and source of reference.
—Statistical Methods in Medical Research
