Verfügbarkeit: Introducing Monte Carlo methods with R

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Titel:	Introducing Monte Carlo methods with R
Von:	Christian P. Robert ; George Casella
Person:	Robert, Christian P. 1961- Verfasser aut Casella, George 1951-2012
Hauptverfassende:	Robert, Christian P. 1961- (VerfasserIn), Casella, George 1951-2012 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Springer 2010
Schriftenreihe:	Use R!
Notation:	MR 2100 QH 239 SK 820 ST 250 ST 601
Schlagwörter:	R > Programm Monte-Carlo-Simulation
Medienzugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018695020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIX, 283 S. graph. Darst.
ISBN:	9781441915757

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface ........................................................ vii List of Figures ................................................. xiii List of Examples ...............................................xvii 1 Basic R Programming ..................................... 1 1.1 Introduction ............................................ 2 1.2 Getting started .......................................... 3 1.3 R objects ............................................... 5 1.3.1 The vector class ................................... 6 1.3.2 The matrix, array, and factor classes .................. 9 1.3.3 The list and data.frame classes ...................... 12 1.4 Probability distributions in R ............................. 14 1.5 Basic and not-so-basic statistics ........................... 14 1.6 Graphical facilities ....................................... 26 1.7 Writing new R functions .................................. 31 1.8 Input and output in R .................................... 35 1.9 Administration of R objects ............................... 36 1.10 The mcsm package ....................................... 36 1.11 Additional exercises ...................................... 37 2 Random Variable Generation .............................. 41 2.1 Introduction ............................................ 42 2.1.1 Uniform simulation ................................ 42 2.1.2 The inverse transform .............................. 44 2.2 General transformation methods ........................... 46 2.2.1 A normal generator ................................ 47 2.2.2 Discrete distributions .............................. 48 2.2.3 Mixture representations ............................ 50 2.3 Accept-reject methods ................................... 51 x Contents 2.4 Additional exercises ...................................... 57 3 Monte Carlo Integration ................................... 61 3.1 Introduction ............................................ 62 3.2 Classical Monte Carlo integration .......................... 65 3.3 Importance sampling ..................................... 69 3.3.1 An arbitrary change of reference measure ............. 69 3.3.2 Sampling importance resampling .................... 75 3.3.3 Selection of the importance function ................. 78 3.4 Additional exercises ...................................... S6 4 Controlling and Accelerating Convergence ................. 89 4.1 Introduction ............................................ 90 4.2 Monitoring variation ..................................... 91 4.3 Asymptotic variance of importance sampling estimators ...... 92 4.4 Effective sample size and perplexity ........................ 98 4.5 Simultaneous monitoring .................................100 4.6 Rao-Blackwellization and deconditioning ...................107 4.7 Acceleration methods .................................... Ш 4.7.1 Correlated simulations ............................. Ill 4.7.2 Antithetic variables ................................113 4.7.3 Control variâtes ...................................116 4.8 Additional exercises ......................................122 5 Monte Carlo Optimization .................................125 5.1 Introduction ............................................126 5.2 Numerical optimization methods ..........................127 5.3 Stochastic search ........................................130 5.3.1 A basic solution ...................................130 5.3.2 Stochastic gradient methods ........................136 5.3.3 Simulated annealing ...............................140 5.4 Stochastic approximation .................................146 5.4.1 Optimizing Monte Carlo approximations .............146 5.4.2 Missing-data models and deniarginalizatiou ...........150 5.4.3 The EM algorithm ................................152 5.4.4 Monte Carlo EM ..................................157 5.5 Additional exercises ......................................163 6 Metropolis—Hastings Algorithms ...........................167 6.1 Introduction ............................................168 6.2 A peek at Markov chain theory ............................168 6.3 Basic Metropolis-Hastings algorithms ......................170 6.3.1 A generic Markov chain Monte Carlo algorithm .......171 6.3.2 The independent Metropolis-Hastings algorithm ......175 6.4 A selection of candidates .................................182 Contents xi 0.4.1 Random walks ....................................182 6.4.2 Alternative candidates .............................185 6.5 Acceptance rates ........................................192 6.6 Additional exercises ......................................195 7 Gibbs Samplers ............................................199 7.1 Introduction ............................................200 7.2 The two-stage Gibbs sampler .............................200 7.3 The multistage Gibbs sampler .............................206 7.4 Missing data and latent variables ..........................209 7.5 Hierarchical structures ...................................221 7.6 Other considerations .....................................224 7.6.1 Reparameterization ................................224 7.6.2 Rao-Blackwellization ..............................227 7.6.3 Metropolis within Gibbs and hybrid strategies ........230 7.6.4 Improper priors ...................................232 7.7 Additional exercises ......................................234 8 Monitoring and Adaptation for MCMC Algorithms ........237 8.1 Introduction ............................................238 8.2 Monitoring what and why ................................238 8.2.1 Convergence to the stationary distribution ............238 8.2.2 Convergence of averages ............................240 8.2.3 Approximating iid sampling ........................240 8.2.4 The coda package .................................241 8.3 Monitoring convergence to stationarity .....................242 8.3.1 Graphical diagnoses ...............................242 8.3.2 Nonparametric tests of stationarity ..................243 8.3.3 Spectral analysis ..................................247 8.4 Monitoring convergence of averages ........................250 8.4.1 Graphical diagnoses ...............................250 8.4.2 Within and between variances ......................253 8.4.3 Effective sample size ...............................255 8.4.4 Fixed-width batch means ...........................257 8.5 Adaptive MCMC ........................................258 8.5.1 Cautions about adaptation .........................258 8.5.2 The amcmc package ................................264 8.6 Additional exercises ......................................267 References .....................................................269 Index of R Terms ..............................................275 Index of Subjects ..............................................279
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author	Robert, Christian P. 1961- Casella, George 1951-2012
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spellingShingle	Robert, Christian P. 1961- Casella, George 1951-2012 Introducing Monte Carlo methods with R R Programm (DE-588)4705956-4 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd
subject_GND	(DE-588)4705956-4 (DE-588)4240945-7
title	Introducing Monte Carlo methods with R
title_auth	Introducing Monte Carlo methods with R
title_exact_search	Introducing Monte Carlo methods with R
title_full	Introducing Monte Carlo methods with R Christian P. Robert ; George Casella
title_fullStr	Introducing Monte Carlo methods with R Christian P. Robert ; George Casella
title_full_unstemmed	Introducing Monte Carlo methods with R Christian P. Robert ; George Casella
title_short	Introducing Monte Carlo methods with R
title_sort	introducing monte carlo methods with r
topic	R Programm (DE-588)4705956-4 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd
topic_facet	R Programm Monte-Carlo-Simulation
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018695020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT robertchristianp introducingmontecarlomethodswithr AT casellageorge introducingmontecarlomethodswithr

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