Morgan Applied Stochastic Modelling, Second Edition

2. Auflage 2011
ISBN: 978-1-4200-1165-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 368 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

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.

Zielgruppe

Undergraduate and graduate students in mathematics and statistics.

Autoren/Hrsg.

Morgan, Byron J.T.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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.