What we usually desire ergodicity results for.

# Handy tricks

Pierre E. Jacob, John O'Leary, Yves F. Atchadé made MCMC estimators without finite-time-bias, which is nice for parallelisation. (JaOA17_)

## Refs

- Cald14: Ben Calderhead (2014) A general construction for parallelizing Metropolis−Hastings algorithms.
*Proceedings of the National Academy of Sciences*, 111(49), 17408–17413. DOI - YoWe10: Ryo Yoshida, Mike West (2010) Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing.
*Journal of Machine Learning Research*, 11(May), 1771–1798. - PrWi98: James Gary Propp, David Bruce Wilson (1998) Coupling from the past: a user’s guide. In Microsurveys in Discrete Probability (Vol. 41, pp. 181–192). Providence, Rhode Island: American Mathematical Society DOI
- LeDL07: S. R. Lele, B. Dennis, F. Lutscher (2007) Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods.
*Ecology Letters*, 10(7), 551. DOI - LeNS10: Subhash R. Lele, Khurram Nadeem, Byron Schmuland (2010) Estimability and likelihood inference for generalized linear mixed models using data cloning.
*Journal of the American Statistical Association*, 105(492), 1617–1625. DOI - PrWi96: James Gary Propp, David Bruce Wilson (1996) Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics. In Random Structures & Algorithms (Vol. 9, pp. 223–252). New York, NY, USA: John Wiley & Sons, Inc. DOI
- RuRV14: Reuven Y. Rubinstein, Ad Ridder, Radislav Vaisman (2014)
*Fast sequential Monte Carlo methods for counting and optimization*. Hoboken, New Jersey: Wiley - DuMo16: Alain Durmus, Eric Moulines (2016) High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm.
*ArXiv:1605.01559 [Math, Stat]*. - Neal04: Radford M. Neal (2004) Improving Asymptotic Variance of MCMC Estimators: Non-reversible Chains are Better.
*ArXiv:Math/0407281*. - DiFr99: Persi Diaconis, David Freedman (1999) Iterated Random Functions.
*SIAM Review*, 41(1), 45–76. DOI - XSLB14: T. Xifara, C. Sherlock, S. Livingstone, S. Byrne, M. Girolami (2014) Langevin diffusions and the Metropolis-adjusted Langevin algorithm.
*Statistics & Probability Letters*, 91(Supplement C), 14–19. DOI - Neal11: Radford M. Neal (2011) MCMC using Hamiltonian dynamics. In Handbook for Markov chain Monte Carlo. Boca Raton: Taylor & Francis
- Liu96: Jun S. Liu (1996) Metropolized independent sampling with comparisons to rejection sampling and importance sampling.
*Statistics and Computing*, 6(2), 113–119. DOI - Neal93: Radford M. Neal (1993) Probabilistic inference using Markov chain Monte Carlo methods (No. Technical Report CRGTR-93-1). Toronto Canada: Department of Computer Science, University of Toronto,
- GiCa11: Mark Girolami, Ben Calderhead (2011) Riemann manifold Langevin and Hamiltonian Monte Carlo methods.
*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, 73(2), 123–214. DOI - RuKr16: Reuven Y. Rubinstein, Dirk P. Kroese (2016)
*Simulation and the Monte Carlo Method*. Hoboken, New Jersey: Wiley - Beta18: Michael Betancourt (2018) The Convergence of Markov chain Monte Carlo Methods: From the Metropolis method to Hamiltonian Monte Carlo.
*Annalen Der Physik*. DOI - RuKr04: Reuven Y Rubinstein, Dirk P Kroese (2004)
*The Cross-Entropy Method a Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning*. New York, NY: Springer New York - BBLG17: Michael Betancourt, Simon Byrne, Sam Livingstone, Mark Girolami (2017) The geometric foundations of Hamiltonian Monte Carlo.
*Bernoulli*, 23(4A), 2257–2298. DOI - NoFo16: Richard A. Norton, Colin Fox (2016) Tuning of MCMC with Langevin, Hamiltonian, and other stochastic autoregressive proposals.
*ArXiv:1610.00781 [Math, Stat]*. - JaOA17: Pierre E. Jacob, John O’Leary, Yves F. Atchadé (2017) Unbiased Markov chain Monte Carlo with couplings.
*ArXiv:1708.03625 [Stat]*.