Voss J. An Introduction to Statistical Computing: A Simulation-based Approach

Wiley, 2013. — 388 p. — ISBN: 1118357728, 9781118357729A comprehensive introduction to sampling-based methods in statistical computing
The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods.
An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques
An Introduction to Statistical Computing:
Fully covers the traditional topics of statistical computing.
Discusses both practical aspects and the theoretical background.
Includes a chapter about continuous-time models.
Illustrates all methods using examples and exercises.
Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online.
Includes an introduction to programming in R.This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught courseList of algorithmsNomenclature
Random number generation
Pseudo random number generators
Discrete distributions
The inverse transform method
Rejection sampling
Transformation of random variables
Special-purpose methods
Summary and further reading
Exercises
Simulating statistical models
Multivariate normal distributions
Hierarchical models
Markov chains
Poisson processes
Summary and further reading
Exercises
Monte Carlo methods
Studying models via simulation
Monte Carlo estimates
Variance reduction methods
Applications to statistical inference
Summary and further reading
Exercises
Markov Chain Monte Carlo methods
The Metropolis–Hastings method
Convergence of Markov Chain Monte Carlo methods
Applications to Bayesian inference
The Gibbs sampler
Reversible Jump Markov Chain Monte Carlo
Summary and further reading
Exercises
Beyond Monte Carlo
Approximate Bayesian Computation
Resampling methods
Summary and further reading
Exercises
Continuous-time models
Time discretisation
Brownian motion
Geometric Brownian motion
Stochastic differential equations
Monte Carlo estimates
Application to option pricing
Summary and further reading
ExercisesAppendix A Probability reminders
Appendix B Programming in R
Appendix C Answers to the exercises