00000cam a22000004i 4500 UP-99796217612665619 Buklod 20180203150953.0 m |o d | ta 180203s2014 xx d r |||| u| 9781118357729 (iLib)UPD-00360912548 DLC DSTC rda eng DMLUC QA 276.4 V66 2014 Voss, Jochen author. An introduction to statistical computing a simulation-based approach Jochen Voss, School of Mathematics, University of Leeds, UK. Chichester, West Sussex Wiley 2014. xii, 382 pages illustrations 26 cm content rdacarrier unmediated rdamedia volume rdacarrier Wiley series in computational statistics Includes bibliographical references (pages 375-377) and index. 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 reading -- Exercises -- 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. Contents note continued: 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 inference -- 3.4.1. 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 method -- 4.4.2. Application to parameter estimation -- 4.4.3. Applications to image processing. Contents note continued: 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 models -- 6.1. 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. Contents note continued: 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 -- A.2. Conditional probability -- A.3. Expectation -- A.4. Limit theorems -- A.5. Further reading -- Appendix B Programming in R -- B.1. General advice -- B.2.R as a Calculator -- B.2.1. Mathematical operations -- B.2.2. Variables -- B.2.3. Data types -- B.3. Programming principles -- B.3.1. Don't repeat yourself! -- B.3.2. Divide and conquer! -- B.3.3. Test your code! -- B.4. Random number generation -- B.5. Summary and further reading -- Exercises -- Appendix C Answers to the exercises -- C.1. Answers for Chapter 1 -- C.2. Answers for Chapter 2 -- C.3. Answers for Chapter 3 -- C.4. Answers for Chapter 4 -- C.5. Answers for Chapter 5 -- C.6. Answers for Chapter 6 -- C.7. Answers for Appendix B. 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. Mathematical statistics Data processing. FO UPD DSTC QA 276.4 V66 2014 Book