Monte Carlo Method

This page contains resources about Monte Carlo Methods, Sampling Methods, Monte Carlo Inference, Stochastic Simulation, Systems Simulation and Computational Modelling.

Subfields and Concepts

 * Monte Carlo techniques
 * Particle Filtering / Sequential Monte Carlo (SMC)
 * Kalman Filtering
 * Importance Sampling
 * Sequential Importance Sampling
 * Rejection Sampling
 * Rao-Blackwellised Particle Filtering (RBPF)
 * Markov Chain Monte Carlo (MCMC)
 * Gibbs Sampling
 * Metropolis–Hastings (MH) Algorithm
 * MH-in-Gibbs / Variable-at-a-time / Metropolis-within-Gibbs / MH-within-Gibbs
 * Hybrid / Hamiltonian Monte Carlo (HMC)
 * No-U-Turn Sampler (NUTS)
 * Simulated Annealing
 * Annealed Importance Sampling
 * Cross-entropy (CE) Method
 * Variance Reductions Techniques (VRT)
 * Antithetic Variables
 * Control variates / Regression sampling
 * Importance Sampling
 * Simulation and Computational Modelling
 * Estimation Theory / Parameter Estimation
 * Stochastic Optimization
 * Model fitting
 * Model selection and evaluation
 * Uncertainty and Sensitivity Analysis

Video Lectures

 * Monte Carlo Simulation for Statistical Inference, Model Selection and Decision Making by Nando de Freitas - VideoLectures.NET
 * Sequential Monte-Carlo Methods by Arnaud Doucet and Nando de Freitas - VideoLectures.NET
 * MCMC Learning by Varun Kanade - VideoLectures.NET
 * Markov Chain Monte Carlo by Ian Murray - VideoLectures.NET

Lecture Notes

 * Monte Carlo Methods by Michael Mascagni
 * Simulation Methods by Alan Genz
 * Stochastic Simulation by Elad Hazan
 * Systems Simulation by Hossein Arsham
 * Lecture: Parameter estimation, uncertainty, model fitting, model selection, and sensitivity and uncertainty analysis by Jamie Lloyd-Smith
 * Lecture: Model Fitting and Error Estimation by Kevin D. Costa

Books and Book Chapters

 * Rubinstein, R. Y., & Kroese, D. P. (2016). Simulation and the Monte Carlo method. 3rd Ed. John Wiley & Sons.
 * Bengio, Y., Goodfellow, I. J., & Courville, A. (2016). "Chapter 17: Monte Carlo Methods". Deep Learning. MIT Press.
 * Theodoridis, S. (2015). "Chapter 14: Monte Carlo Methods". Machine Learning: A Bayesian and Optimization Perspective . Academic Press.
 * Theodoridis, S. (2015). "Chapter 17: Particle Filtering". Machine Learning: A Bayesian and Optimization Perspective . Academic Press.
 * Law, A. M., Kelton (2014). Simulation modeling and analysis. 5th Ed. McGraw-Hill.
 * Owen, A. B. (2013). Monte Carlo Theory, Methods and Examples. (link)
 * Durbin, J., & Koopman, S. J. (2012). Time series analysis by state space methods. Oxford University Press.
 * Murphy, K. P. (2012). "Chapter 23: Monte Carlo inference". Machine Learning: A Probabilistic Perspective. MIT Press.
 * Barber, D. (2012). "Chapter 27: Sampling". Bayesian Reasoning and Machine Learning. Cambridge University Press.
 * Ross, S. M. (2012). Simulation. 5th Ed. Academic Press.
 * Brooks, S., Gelman, A., Jones, G., & Meng, X. L. (Eds.). (2011). Handbook of Markov Chain Monte Carlo. CRC press.
 * Kroese, D. P., Taimre, T., & Botev, Z. I. (2011). Handbook of monte carlo methods. John Wiley & Sons.
 * Robert, C., & Casella, G. (2010). Monte Carlo statistical methods. Springer Science & Business Media.


 * Koller, D., & Friedman, N. (2009). "Chapter 12: Particle-Based Approximate Inference". Probabilistic Graphical Models. MIT Press.
 * Asmussen, S., & Glynn, P. W. (2007). Stochastic simulation: algorithms and analysis. Springer Science & Business Media.


 * Bishop, C. M. (2006). "Chapter 11: Sampling Methods". Pattern Recognition and Machine Learning. Springer.


 * MacKay, D. J. (2003). "Chapter 29: Monte Carlo Methods" Information Theory, Inference and Learning Algorithms. Cambridge University Press.
 * Rubinstein, R. Y., & Melamed, B. (1998). Modern simulation and modeling. John Wiley & Sons.
 * Gilks, W. R., Richardson, S. & Spiegelhalter, D. J. (eds): Markov Chain Monte Carlo in Practice. Chapman & Hall/CRC, 1996.

Scholarly Articles

 * Neal, R. M. (1993). Probabilistic inference using Markov chain Monte Carlo methods.
 * MacKay, D. J. (1998). Introduction to monte carlo methods. In Learning in graphical models (pp. 175-204). Springer Netherlands.

Tutorials

 * MCMC Review

Software

 * MCMC toolbox - MATLAB
 * Ensemble MCMC sampler - MATLAB
 * emce - Python
 * PyMC3 - Python

Other Resources

 * MCMC sampling for dummies - Python
 * MCMC programming in R, Python, Java and C
 * Video lectures on Monte Carlo - VideoLectures.NET
 * Monte Carlo, and Other Kinds of Stochastic Simulation - Notebook