The Generalized Splitting Method

Zdravko Botev

ISBN 10: 3838397266 / ISBN 13: 9783838397269

Published by LAP LAMBERT Academic Publishing Sep 2010, 2010

About this Item

Neuware -We describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. The second part of the thesis presents a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug- in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.Books on Demand GmbH, Überseering 33, 22297 Hamburg 140 pp. Englisch.

Seller Inventory # 9783838397269

Bibliographic Details

• Title: The Generalized Splitting Method
• Publisher: LAP LAMBERT Academic Publishing Sep 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 3838397266
• ISBN 13: 9783838397269
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 9D millimeters 220 millimeters width by 150 millimeters height by 9 millimeters depth
• Weight: 227 grams

About this title

Synopsis

We describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. The second part of the thesis presents a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug- in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.

About the Author

Dr. Botev has graduated from the University of Queensland, Australia with First class Honors degree and a university medal in 2005. He completed his Phd in 2009 and since then he has lectured at the University of Queensland. Currently, he is a postdoctoral fellow at the University of Montreal.