An Introduction to Statistical Computing; Contents; List of algorithms; Preface; Nomenclature; 1 Random number generation; 1.1 Pseudo random number generators; 1.1.1 The linear congruential generator; 1.1.2 Quality of pseudo random number generators; 1.1.3 Pseudo random number generators in practice; 1.2 Discrete distributions; 1.3 The inverse transform method; 1.4 Rejection sampling; 1.4.1 Basic rejection sampling; 1.4.2 Envelope rejection sampling; 1.4.3 Conditional distributions; 1.4.4 Geometric interpretation; 1.5 Transformation of random variables; 1.6 Special-purpose methods
1.7 Summary and further readingExercises; 2 Simulating statistical models; 2.1 Multivariate normal distributions; 2.2 Hierarchical models; 2.3 Markov chains; 2.3.1 Discrete state space; 2.3.2 Continuous state space; 2.4 Poisson processes; 2.5 Summary and further reading; Exercises; 3 Monte Carlo methods; 3.1 Studying models via simulation; 3.2 Monte Carlo estimates; 3.2.1 Computing Monte Carlo estimates; 3.2.2 Monte Carlo error; 3.2.3 Choice of sample size; 3.2.4 Refined error bounds; 3.3 Variance reduction methods; 3.3.1 Importance sampling; 3.3.2 Antithetic variables; 3.3.3 Control variates
3.4 Applications to statistical inference3.4.1 Point estimators; 3.4.2 Confidence intervals; 3.4.3 Hypothesis tests; 3.5 Summary and further reading; Exercises; 4 Markov Chain Monte Carlo methods; 4.1 The Metropolis-Hastings method; 4.1.1 Continuous state space; 4.1.2 Discrete state space; 4.1.3 Random walk Metropolis sampling; 4.1.4 The independence sampler; 4.1.5 Metropolis-Hastings with different move types; 4.2 Convergence of Markov Chain Monte Carlo methods; 4.2.1 Theoretical results; 4.2.2 Practical considerations; 4.3 Applications to Bayesian inference; 4.4 The Gibbs sampler
4.4.1 Description of the method4.4.2 Application to parameter estimation; 4.4.3 Applications to image processing; 4.5 Reversible Jump Markov Chain Monte Carlo; 4.5.1 Description of the method; 4.5.2 Bayesian inference for mixture distributions; 4.6 Summary and further reading; 4.6 Exercises; 5 Beyond Monte Carlo; 5.1 Approximate Bayesian Computation; 5.1.1 Basic Approximate Bayesian Computation; 5.1.2 Approximate Bayesian Computation with regression; 5.2 Resampling methods; 5.2.1 Bootstrap estimates; 5.2.2 Applications to statistical inference; 5.3 Summary and further reading; Exercises
6 Continuous-time models6.1 Time discretisation; 6.2 Brownian motion; 6.2.1 Properties; 6.2.2 Direct simulation; 6.2.3 Interpolation and Brownian bridges; 6.3 Geometric Brownian motion; 6.4 Stochastic differential equations; 6.4.1 Introduction; 6.4.2 Stochastic analysis; 6.4.3 Discretisation schemes; 6.4.4 Discretisation error; 6.5 Monte Carlo estimates; 6.5.1 Basic Monte Carlo; 6.5.2 Variance reduction methods; 6.5.3 Multilevel Monte Carlo estimates; 6.6 Application to option pricing; 6.7 Summary and further reading; Exercises; Appendix A Probability reminders; A.1 Events and probability
Summary
"This is a book about exploring random systems using computer simulation and thus, this book combines two different topic areas which have always fascinated me: the mathematical theory of probability and the art of programming computers"-- Provided by publisher
Bibliography
Includes bibliographical references and index
Notes
Print version record and CIP data provided by publisher; resource not viewed
