Monte Carlo Strategies in Scientific Computing

1. Auflage 2001, 2. printing 2008
ISBN: 978-0-387-76369-9
Verlag: Springer

Buch, Englisch, 344 Seiten, Format (B × H): 154 mm x 236 mm, Gewicht: 1130 g

Reihe: Springer Series in Statistics

This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.

Zielgruppe

Research

Autoren/Hrsg.

Liu, Jun S

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Enzyklopädien, Nachschlagewerke, Wörterbücher
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

1 Introduction and Examples.- 2 Basic Principles: Rejection, Weighting, and Others.- 3 Theory of Sequential Monte Carlo.- 4 Sequential Monte Carlo in Action.- 5 Metropolis Algorithm and Beyond.- 6 The Gibbs Sampler.- 7 Cluster Algorithms for the Ising Model.- 8 General Conditional Sampling.- 9 Molecular Dynamics and Hybrid Monte Carlo.- 10 Multilevel Sampling and Optimization Methods.- 11 Population-Based Monte Carlo Methods.- 12 Markov Chains and Their Convergence.- 13 Selected Theoretical Topics.- A Basics in Probability and Statistics.- A.1 Basic Probability Theory.- A.1.1 Experiments, events, and probability.- A.1.2 Univariate random variables and their properties.- A.1.3 Multivariate random variable.- A.1.4 Convergence of random variables.- A.2 Statistical Modeling and Inference.- A.2.1 Parametric statistical modeling.- A.2.2 Frequentist approach to statistical inference.- A.2.3 Bayesian methodology.- A.3 Bayes Procedure and Missing Data Formalism.- A.3.1 The joint and posterior distributions.- A.3.2 The missing data problem.- A.4 The Expectation-Maximization Algorithm.- References.- Author Index.