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Bayesian Monte Carlo

2003

Conference Paper

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We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation of prior knowledge, such as smoothness of the integrand, into the estimation. In a simple problem we show that this outperforms any classical importance sampling method. We also attempt more challenging multidimensional integrals involved in computing marginal likelihoods of statistical models (a.k.a. partition functions and model evidences). We find that Bayesian Monte Carlo outperformed Annealed Importance Sampling, although for very high dimensional problems or problems with massive multimodality BMC may be less adequate. One advantage of the Bayesian approach to Monte Carlo is that samples can be drawn from any distribution. This allows for the possibility of active design of sample points so as to maximise information gain.

Author(s): Rasmussen, CE. and Ghahramani, Z.
Book Title: Advances in Neural Information Processing Systems 15
Journal: Advances in Neural Information Processing Systems 15
Pages: 489-496
Year: 2003
Month: October
Day: 0
Editors: Becker, S. , S. Thrun, K. Obermayer
Publisher: MIT Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: Sixteenth Annual Conference on Neural Information Processing Systems (NIPS 2002)
Event Place: Vancouver, BC, Canada

Address: Cambridge, MA, USA
Digital: 0
ISBN: 0-262-02550-7
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{2104,
  title = {Bayesian Monte Carlo},
  author = {Rasmussen, CE. and Ghahramani, Z.},
  journal = {Advances in Neural Information Processing Systems 15},
  booktitle = {Advances in Neural Information Processing Systems 15},
  pages = {489-496},
  editors = {Becker, S. , S. Thrun, K. Obermayer},
  publisher = {MIT Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = oct,
  year = {2003},
  month_numeric = {10}
}