Further Reading

The following is the non-exhaustive list of useful sources for learning more about Monte Carlo methods. Some of the code in monte-library has been written based on mathematical formulae from some of these sources.

General

[1] Ntzoufras, I. (2009). Bayesian Modelling Using WinBUGS. Wiley.

[2] Metropolis, N., & Ulam, S. (1949). The Monte Carlo Method. Journal of the American Statistical Association, 44(247), 335–341. https://doi.org/10.1080/01621459.1949.10483310

Metropolis

[3] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (2004). Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics, 21(6), 1087. https://doi.org/10.1063/1.1699114

[4] Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109. https://doi.org/10.1093/BIOMET/57.1.97

[5] Hartig, F. (n.d.). A simple Metropolis-Hastings MCMC in R | theoretical ecology. Retrieved February 15, 2023, from https://theoreticalecology.wordpress.com/2010/09/17/metropolis-hastings-mcmc-in-r/

[6] Dirty Quant @YouTube. (n.d.). The Metropolis-Hastings Algorithm (MCMC in Python) - YouTube. Retrieved February 15, 2023, from https://www.youtube.com/watch?v=MxI78mpq_44

[7] TWEAG Software Innovation Lab. (n.d.). Markov chain Monte Carlo (MCMC) Sampling, Part 1: The Basics - Tweag. Retrieved February 15, 2023, from https://www.tweag.io/blog/2019-10-25-mcmc-intro1/

[8] Urbanevych, V. (n.d.). VU | Bayesian linear regression and Metropolis-Hastings sampler. Retrieved February 15, 2023, from https://vitaliiur.github.io/blog/2021/linreg/

Gibbs Sampler

[9] Geman, S., & Geman, D. (1984). Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-6(6), 721–741. https://doi.org/10.1109/TPAMI.1984.4767596

[10] Campbell, K. R. (n.d.). Gibbs sampling for Bayesian linear regression in Python | Kieran R Campbell - blog. Retrieved February 15, 2023, from https://kieranrcampbell.github.io/blog/2016/05/15/gibbs-sampling-bayesian-linear-regression.html

Hamiltonian Monte Carlo

[11] Betancourt, M. (2017). A Conceptual Introduction to Hamiltonian Monte Carlo. https://doi.org/10.48550/arxiv.1701.02434

[12] Neal, R. M. (2012). MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo, 1–592. https://doi.org/10.1201/b10905

[13] Stan. (n.d.). 15.1 Hamiltonian Monte Carlo | Stan Reference Manual. Retrieved February 15, 2023, from https://mc-stan.org/docs/reference-manual/hamiltonian-monte-carlo.html

[14] Clark, M. (n.d.). Hamiltonian Monte Carlo | Model Estimation by Example. Retrieved February 15, 2023, from https://m-clark.github.io/models-by-example/hamiltonian-monte-carlo.html

[15] Richard. (n.d.). Markov Chains: Why Walk When You Can Flow? | Elements of Evolutionary Anthropology. Retrieved February 15, 2023, from http://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/