Radford Neal's Research: Markov Chain Monte Carlo

Markov Chain Monte Carlo (MCMC) is a computational technique long used in statistical physics, now all the rage as a way of doing Bayesian inference. In this method, we make Monte Carlo estimates of interesting quantities using a sample of points generated by a Markov chain that we design to have the equilibrium distribution that we are interested in.

I have written a comprehensive review of Markov chain Monte Carlo methods, with particular attention to their applications to problems in artificial intelligence:

Neal, R. M. (1993) Probabilistic Inference Using Markov Chain Monte Carlo Methods, Technical Report CRG-TR-93-1, Dept. of Computer Science, University of Toronto, 144 pages: abstract, contents, postscript, pdf.
The following paper is also of general interest:
Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. M. (1998) ``Markov Chain Monte Carlo in Practice: A Roundtable Discussion'', The American Statistician, vol. 52, pp. 93-100.

Other papers of mine with interesting Markov chain Monte Carlo stuff:
Neal, R. M. (2005) ``Estimating ratios of normalizing constants using Linked Importance Sampling'', Technical Report No. 0511, Dept. of Statistics, University of Toronto, 37 pages: abstract, postscript, pdf, associated software.

Jain, S. and Neal, R. M. (2005) ``Splitting and merging components of a nonconjugate Dirichlet process mixture model'', Technical Report No. 0507, Dept. of Statistics, 37 pages: abstract, postscript, pdf, associated references.

Neal, R. M. (2005) ``The short-cut Metropolis method'', Technical Report No. 0506, Dept. of Statistics, University of Toronto, 28 pages: abstract, postscript, pdf, associated software.

Neal, R. M. (2004) ``Taking bigger Metropolis steps by dragging fast variables'', Technical Report No. 0411, Dept. of Statistics, University of Toronto, 9 pages: abstract, postscript, pdf, associated software.

Neal, R. M. (2004) ``Improving asymptotic variance of MCMC estimators: Non-reversible chains are better'', Technical Report No. 0406, Dept. of Statistics, University of Toronto, 25 pages: abstract, postscript, pdf.

Neal, R. M. (2003) ``Markov chain sampling for non-linear state space models using embedded hidden Markov models'', Technical Report No. 0304, Dept. of Statistics, University of Toronto, 9 pages: abstract, postscript, pdf.

Pinto, R. L. and Neal, R. M. (2001) ``Improving Markov chain Monte Carlo estimators by coupling to an approximating chain'', Technical Report No. 0101, Dept. of Statistics, University of Toronto, 13 pages: abstract, postscript, pdf.

Neal, R. M. (2000) ``Slice sampling'', Technical Report No. 2005, Dept. of Statistics, University of Toronto, 40 pages: abstract, postscript, pdf, associated references, associated software.

Jain, S. and Neal, R. M. (2000) ``A Split-Merge Markov Chain Monte Carlo Procedure for the Dirichlet Process Mixture Model'', Technical Report No. 2003, Dept. of Statistics (July 2000), 32 pages: abstract, postscript, pdf, associated references.

Neal, R. M. (2002) ``Circularly-coupled Markov chain sampling'', Technical Report No. 9910 (revised), Dept. of Statistics, University of toronto, 49 pages: abstract, postscript, pdf.

Neal, R. M. (1998) ``Annealed importance sampling'', Technical Report No. 9805 (revised), Dept. of Statistics, University of Toronto, 25 pages: abstract, associated references, postscript, pdf.

Neal, R. M. (1998) ``Suppressing random walks in Markov chain Monte Carlo using ordered overrelaxation'', in M. I. Jordan (editor) Learning in Graphical Models, pp. 205-225, Dordrecht: Kluwer Academic Publishers: abstract, associated references, postscript, pdf.

Diaconis, P., Holmes, S., and Neal, R. M. (1997) ``Analysis of a non-reversible Markov chain sampler'', Technical Report BU-1385-M, Biometrics Unit, Cornell University, 26 pages: abstract, associated reference, postscript, pdf.

Neal, R. M. (1994) ``Sampling from multimodal distributions using tempered transitions'', Technical Report No. 9421, Dept. of Statistics, University of Toronto, 22 pages: abstract, associated reference, postscript, pdf.

Neal, R. M. (1996) Bayesian Learning for Neural Networks, Lecture Notes in Statistics No. 118, New York: Springer-Verlag: blurb, associated references, associated software.

Neal, R. M. (1994) ``An improved acceptance procedure for the hybrid Monte Carlo algorithm'', Journal of Computational Physics, vol. 111, pp. 194-203: abstract.

Neal, R. M. (1992) ``Bayesian training of backpropagation networks by the hybrid Monte Carlo method'', Technical Report CRG-TR-92-1, Dept. of Computer Science, University of Toronto, 21 pages: abstract, postscript, pdf, associated references.

Papers applying Markov chain Monte Carlo, but less interesting from the point of view of Markov chain Monte Carlo per se:
Neal, R. M. (2001) ``Transferring prior information between models using imaginary data'', Technical Report No. 0108, Dept. of Statistics, University of Toronto, 29 pages: abstract, postscript, pdf, associated software.

Neal, R. M. (1998) ``Markov chain sampling methods for Dirichlet process mixture models'', Technical Report No. 9815, Dept. of Statistics, University of toronto, 17 pages: abstract, postscript, pdf, associated reference, associated software.

Neal, R. M. (1997) ``Monte Carlo implementation of Gaussian process models for Bayesian regression and classification'', Technical Report No. 9702, Dept. of Statistics, University of Toronto, 24 pages: abstract, postscript, pdf, associated software.

Neal, R. M. (1991) ``Bayesian mixture modeling by Monte Carlo simulation'', Technical Report CRG-TR-91-2, Dept. of Computer Science, University of Toronto, 23 pages: abstract, postscript, pdf, associated references.

Neal, R. M. (1990) ``Learning stochastic feedforward networks'', Technical Report CRG-TR-90-7, Dept. of Computer Science, University of Toronto, 34 pages: abstract, postscript, pdf, associated reference.


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