Reflections on Bayesian inference and Markov chain Monte Carlo

Bayesian inference and Markov chain Monte Carlo methods are vigorous areas of statistical research. Here we reflect on some recent developments and future directions in these fields.

[1]  Nicholas G. Tawn,et al.  Skew brownian motion and complexity of the alps algorithm , 2020, Journal of Applied Probability.

[2]  Edward I. George,et al.  Bayes and big data: the consensus Monte Carlo algorithm , 2016, Big Data and Information Theory.

[3]  Taylor G. Asher,et al.  High-fidelity hurricane surge forecasting using emulation and sequential experiments , 2021 .

[4]  J. Ioannidis,et al.  COVID-19 antibody seroprevalence in Santa Clara County, California , 2021, International journal of epidemiology.

[5]  Evgeny Levi,et al.  Finding our Way in the Dark: Approximate MCMC for Approximate Bayesian Methods , 2019, Bayesian Analysis.

[6]  I. Heid,et al.  Analysis of COVID-19 case numbers: adjustment for diagnostic misclassification on the example of German case reporting data , 2020 .

[7]  Igor Burstyn,et al.  Towards reduction in bias in epidemic curves due to outcome misclassification through Bayesian analysis of time-series of laboratory test results: case study of COVID-19 in Alberta, Canada and Philadelphia, USA , 2020, BMC Medical Research Methodology.

[8]  A. Gelman,et al.  Bayesian Analysis of Tests with Unknown Specificity and Sensitivity , 2020, medRxiv.

[9]  P. Gustafson,et al.  Bayesian adjustment for preferential testing in estimating the COVID-19 infection fatality rate: Theory and methods , 2020, 2005.08459.

[10]  A. Mertens,et al.  Substantial underestimation of SARS-CoV-2 infection in the United States , 2020, Nature Communications.

[11]  P. Gustafson,et al.  Towards reduction in bias in epidemic curves due to outcome misclassification through Bayesian analysis of time-series of laboratory test results: Case study of COVID-19 in Alberta, Canada and Philadelphia, USA , 2020, medRxiv.

[12]  Daniel Simpson,et al.  Asynchronous Gibbs Sampling , 2015, AISTATS.

[13]  Alexandre Bouchard-Cot'e,et al.  Blang: Bayesian declarative modelling of arbitrary data structures. , 2019 .

[14]  Wu Changye,et al.  Parallelising MCMC via Random Forests , 2019 .

[15]  Yanan Fan,et al.  Handbook of Approximate Bayesian Computation , 2018 .

[16]  Huidong Jin,et al.  Emulator-enabled approximate Bayesian computation (ABC) and uncertainty analysis for computationally expensive groundwater models , 2018, Journal of Hydrology.

[17]  Christopher C. Drovandi,et al.  Approximating the Likelihood in ABC , 2018, Handbook of Approximate Bayesian Computation.

[18]  Michael Gertz,et al.  Numerically stable parallel computation of (co-)variance , 2018, SSDBM.

[19]  Christopher C Drovandi,et al.  ABC and Indirect Inference , 2018, Handbook of Approximate Bayesian Computation.

[20]  S. A. Sisson,et al.  Overview of Approximate Bayesian Computation , 2018, 1802.09720.

[21]  Chris Sherlock,et al.  Merging MCMC Subposteriors through Gaussian-Process Approximations , 2016, Bayesian Analysis.

[22]  R. Kohn,et al.  Speeding Up MCMC by Efficient Data Subsampling , 2014, Journal of the American Statistical Association.

[23]  James P. Hobert,et al.  Asymptotically Stable Drift and Minorization for Markov Chains with Application to Albert and Chib's Algorithm , 2017 .

[24]  J. Rosenthal,et al.  Complexity results for MCMC derived from quantitative bounds , 2017, The Annals of Applied Probability.

[25]  David T. Frazier,et al.  Bayesian Synthetic Likelihood , 2017, 2305.05120.

[26]  C. Robert,et al.  Inference in generative models using the Wasserstein distance , 2017, 1701.05146.

[27]  Jiqiang Guo,et al.  Stan: A Probabilistic Programming Language. , 2017, Journal of statistical software.

[28]  Gareth O. Roberts,et al.  Complexity bounds for Markov chain Monte Carlo algorithms via diffusion limits , 2016, Journal of Applied Probability.

[29]  Trevor Campbell,et al.  Coresets for Scalable Bayesian Logistic Regression , 2016, NIPS.

[30]  Radu V. Craiu,et al.  Likelihood inflating sampling algorithm , 2016, 1605.02113.

[31]  Haavard Rue,et al.  Bayesian Computing with INLA: A Review , 2016, 1604.00860.

[32]  David M. Blei,et al.  Variational Inference: A Review for Statisticians , 2016, ArXiv.

[33]  Dennis Prangle,et al.  Summary Statistics in Approximate Bayesian Computation , 2015, 1512.05633.

[34]  B. Rajaratnam,et al.  MCMC-Based Inference in the Era of Big Data: A Fundamental Analysis of the Convergence Complexity of High-Dimensional Chains , 2015, 1508.00947.

[35]  Martin J. Wainwright,et al.  On the Computational Complexity of High-Dimensional Bayesian Variable Selection , 2015, ArXiv.

[36]  Paul Gustafson,et al.  Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data , 2015 .

[37]  Dieter Gerten,et al.  Emulating global climate change impacts on crop yields , 2015 .

[38]  C. Andrieu,et al.  Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms , 2012, 1210.1484.

[39]  Luke Bornn,et al.  One Pseudo-Sample is Enough in Approximate Bayesian Computation MCMC , 2014 .

[40]  Chong Wang,et al.  Asymptotically Exact, Embarrassingly Parallel MCMC , 2013, UAI.

[41]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[42]  Xiangyu Wang,et al.  Parallelizing MCMC via Weierstrass Sampler , 2013, 1312.4605.

[43]  J. Rosenthal,et al.  Convergence rate of Markov chain methods for genomic motif discovery , 2013, 1303.2814.

[44]  Julien Cornebise,et al.  On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo , 2011, Statistical applications in genetics and molecular biology.

[45]  Anthony Lee,et al.  On the choice of MCMC kernels for approximate Bayesian computation with SMC samplers , 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

[46]  Paul Fearnhead,et al.  Constructing summary statistics for approximate Bayesian computation: semi‐automatic approximate Bayesian computation , 2012 .

[47]  Jean-Michel Marin,et al.  Approximate Bayesian computational methods , 2011, Statistics and Computing.

[48]  Anthony N. Pettitt,et al.  Discussion of : constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation , 2012 .

[49]  Elizabeth Thompson,et al.  MCMC in the Analysis of Genetic Data on Related Individuals , 2011 .

[50]  Andrew Gelman,et al.  Handbook of Markov Chain Monte Carlo , 2011 .

[51]  Radford M. Neal.  MCMC Using Hamiltonian Dynamics , 2011, 1206.1901.

[52]  S. Wood.  Statistical inference for noisy nonlinear ecological dynamic systems , 2010, Nature.

[53]  Cliburn Chan,et al.  Understanding GPU Programming for Statistical Computation: Studies in Massively Parallel Massive Mixtures , 2010, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[54]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[55]  D. Woodard,et al.  Conditions for Rapid and Torpid Mixing of Parallel and Simulated Tempering on Multimodal Distributions , 2009, 0906.2341.

[56]  D. Woodard,et al.  Sufficient Conditions for Torpid Mixing of Parallel and Simulated Tempering , 2009 .

[57]  C. Andrieu,et al.  The pseudo-marginal approach for efficient Monte Carlo computations , 2009, 0903.5480.

[58]  Mark M. Tanaka,et al.  Sequential Monte Carlo without likelihoods , 2007, Proceedings of the National Academy of Sciences.

[59]  P. Baxendale.  Renewal theory and computable convergence rates for geometrically ergodic Markov chains , 2005, math/0503515.

[60]  Darren J. Wilkinson,et al.  Parallel Bayesian Computation , 2005 .

[61]  Galin L. Jones,et al.  Sufficient burn-in for Gibbs samplers for a hierarchical random effects model , 2004, math/0406454.

[62]  Kathryn B. Laskey,et al.  Population Markov Chain Monte Carlo , 2004, Machine Learning.

[63]  Paul Marjoram,et al.  Markov chain Monte Carlo without likelihoods , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[64]  C. Manski.  Partial Identification of Probability Distributions , 2003 .

[65]  J. Rosenthal.  QUANTITATIVE CONVERGENCE RATES OF MARKOV CHAINS: A SIMPLE ACCOUNT , 2002 .

[66]  J. Rosenthal,et al.  Optimal scaling for various Metropolis-Hastings algorithms , 2001 .

[67]  Gareth O. Roberts,et al.  Corrigendum to : Bounds on regeneration times and convergence rates for Markov chains , 2001 .

[68]  Galin L. Jones,et al.  Honest Exploration of Intractable Probability Distributions via Markov Chain Monte Carlo , 2001 .

[69]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[70]  R. Tweedie,et al.  Bounds on regeneration times and convergence rates for Markov chains fn1 fn1 Work supported in part , 1999 .

[71]  Sally Rosenthal,et al.  Parallel computing and Monte Carlo algorithms , 1999 .

[72]  J. Rosenthal,et al.  Optimal scaling of discrete approximations to Langevin diffusions , 1998 .

[73]  A. Gelman,et al.  Weak convergence and optimal scaling of random walk Metropolis algorithms , 1997 .

[74]  Jeffrey S. Rosenthal,et al.  Analysis of the Gibbs Sampler for a Model Related to James-stein Estimators , 2007 .

[75]  J. Rosenthal.  RATES OF CONVERGENCE FOR GIBBS SAMPLING FOR VARIANCE COMPONENT MODELS , 1995 .

[76]  J. Rosenthal.  Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo , 1995 .

[77]  S. Meyn,et al.  Computable Bounds for Geometric Convergence Rates of Markov Chains , 1994 .

[78]  Walter R. Gilks,et al.  A Language and Program for Complex Bayesian Modelling , 1994 .

[79]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[80]  Mark J. Schervish.  Applications of Parallel Computation to Statistical Inference , 1988 .

[81]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[82]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[83]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[84]  D. Woodard,et al.  Conditions for Torpid Mixing of Parallel and Simulated Tempering on Multimodal Distributions , 2022 .