This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.
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4735
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Maximum Likelihood from incomplete data via the EM algorithm
– Dempster, Laird, et al.
- 1977
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2439
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
– Geman, Geman
- 1984
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2331
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Optimization by Simulated Annealing
– Kirkpatrick, Gelatt, et al.
- 1983
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1245
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Equation of State Calculations by Fast Computing Machines
– Metropolis, Rosenbluth, et al.
- 1953
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1064
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The PageRank Citation Ranking: Bringing Order to the Web
– Page, Brin, et al.
- 1999
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645
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Monte Carlo sampling methods using Markov chains and their applications
– Hastings
- 1970
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557
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Novel approach to nonlinear/non-Gaussian Bayesian state estimation
– Gordon, Salmond, et al.
- 1993
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479
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Markov chains for exploring posterior distributions (with Discussion
– Tierney
- 1994
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450
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A maximisation technique occurring in the statistical analysis of probabilistic functions of Markov chains
– Baum, Soules, et al.
- 1970
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435
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Contour tracking by stochastic propagation of conditional density
– Isard, Blake
- 1996
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434
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Sampling-based approaches to calculating marginal densities
– Gelfand, Smith
- 1990
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427
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Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
– Green
- 1995
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423
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Sequential Monte Carlo Methods in Practice
– Doucet, Freitas, et al.
- 2001
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422
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Bayesian Learning for Neural Networks
– Neal
- 1996
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373
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Monte Carlo Statistical Methods
– Robert, Casella
- 2004
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344
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Probabilistic inference using Markov chain Monte Carlo methods
– Neal
- 1993
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308
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Markov Chain Monte Carlo in Practice
– Gilks, Richardson, et al.
- 1996
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301
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On Sequential Monte Carlo Sampling Methods for Bayesian Filtering
– Doucet, Godsill, et al.
- 2000
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278
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The calculation of posterior distributions by data augmentation (with discussion
– TANNER, W
- 1987
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270
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The infinite hidden markov model
– Beal, Ghahramani, et al.
- 2002
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265
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The world–wide web
– Berners–Lee, Cailliau, et al.
- 1994
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263
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Filtering via simulation: Auxiliary particle Þlters
– Pitt, Shephard
- 1999
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257
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P.: On bayesian analysis of mixtures with an unknown number of components
– Richardson, Green
- 1996
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257
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Simulation and the Monte Carlo method
– Rubinstein
- 1981
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249
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Exactly solved models in statistical mechanics
– Baxter
- 1982
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240
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R.Tweedie, Markov Chains and Stochastic Stability
– Meyn
- 1994
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190
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A Polynomial-time Approximation Algorithm for the Permanent of a Matrix with Non-Negative entries
– Jerrum, Sinclair, et al.
- 2001
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186
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Bayesian Inference in Econometric Models using Monte Carlo Integration
– Geweke
- 1989
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185
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Bayesian analysis of binary and polychotomous response data
– Albert, Chib
- 1993
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170
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Bayesian density estimation and inference using mixtures
– Escobar, West
- 1995
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164
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The markov chain monte carlo method: An approach to approximate counting and integration
– Jerrum, Sinclair
- 1997
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156
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On Gibbs sampling for state space models
– Carter, Kohn
- 1994
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155
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On sequential simulation-based methods for Bayesian Þltering
– Doucet
- 1998
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149
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Nonuniversal critical dynamics in Monte Carlo simulations
– Swendsen, Wang
- 1987
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148
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Rao-Blackwellised particle filtering for dynamic Bayesian networks
– Doucet, Freitas, et al.
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143
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Monte Carlo Strategies in Scientific Computing
– Liu
- 2001
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126
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Stochastic simulation algorithms for dynamic probabilistic networks
– Kanazawa, Koller, et al.
- 1995
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113
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Using the SIR algorithm to simulate posterior distributions
– Rubin
- 1988
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103
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Image segmentation by data-driven markov chain monte carlo
– Tu, Zhu
- 1989
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96
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Rates of convergence of the Hastings and Metropolis algorithms
– Mengersen, Tweedie
- 1996
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95
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Rao-Blackewellization of sampling schemes
– Casella, Robert
- 1996
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93
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Bayesian computation and stochastic systems
– Besag, Green, et al.
- 1995
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90
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Metropolis light transport
– Veach, Guibas
- 1997
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84
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Monte Carlo Methods
– Kalos, Whitlock
- 1986
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78
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The Monte Carlo method
– Metropolis, Ulam
- 1949
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78
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The unscented particle filter
– Merwe, Freitas, et al.
- 2000
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76
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A language and program for complex Bayesian modeling
– Gilks, Thomas, et al.
- 1994
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74
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A random polynomial-time algorithm for approximating the volume of convex bodies
– Dyer, Frieze, et al.
- 1991
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74
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Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
– Roberts, Tweedie
- 1996
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74
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A monte carlo implementation of the EM algorithm and the poor man's data augmentation algorithms
– Wei, Tanner
- 1990
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