Applied stochastic modelling

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 ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributions BootstrapMonte Carlo testingBayesian Methods and MCMC Basic Bayes Three academic examples The Gibbs sampler The Metropolis-Hastings algorithm A hybrid approachThe data augmentation algorithm Model probabilities Model averaging Reversible jump MCMC (RJMCMC)General Families of Models Common structureGeneralised 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 IndexDiscussions and Exercises appear at the end of each chapter.