Highlighting modern computational methods, Applied Stochastic Modelling, Second Edition provides students with the practical experience of scientific computing in applied statistics through a range of interesting real-world applications. It also successfully revises standard probability and statistical theory. Along with an updated bibliography and improved figures, this edition offers numerous updates throughout.
New to the Second Edition
- An extended discussion on Bayesian methods
- A large number of new exercises
- A new appendix on computational methods
The book covers both contemporary and classical aspects of statistics, including survival analysis, Kernel density estimation, Markov chain Monte Carlo, hypothesis testing, regression, bootstrap, and generalised linear models. Although the book can be used without reference to computational programs, the author provides the option of using powerful computational tools for stochastic modelling. All of the data sets and MATLAB® and R programs found in the text as well as lecture slides and other ancillary material are available for download at www.crcpress.com
Continuing in the bestselling tradition of its predecessor, this textbook remains an excellent resource for teaching students how to fit stochastic models to data.
Table of Contents
Introduction and Examples
Examples of data sets
Basic Model Fitting
Maximum-likelihood estimation for a geometric model
Maximum-likelihood for the beta-geometric model
What is a model for?
MATLAB: graphs and finite differences
Deterministic search methods
Stochastic search methods
Accuracy and a hybrid approach
Basic Likelihood Tools
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
Regression and influence
The EM algorithm
Alternative methods of model fitting
Simulating random variables
Monte Carlo inference
Estimating sampling distributions
Monte Carlo testing
Bayesian Methods and MCMC
Three academic examples
The Gibbs sampler
The Metropolis–Hastings algorithm
A hybrid approach
The data augmentation algorithm
Reversible jump MCMC (RJMCMC)
General Families of Models
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
Discussions and Exercises appear at the end of each chapter.
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 Society
I 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, Technometrics
A useful tool for both applied statisticians and stochastic model users of other fields, such as biologists, sociologists, geologists, and economists.
The 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