On computational tools for Bayesian data analysis

While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte Carlo methods and more recently Approximate Bayesian Computation techniques have considerably increased the potential for Bayesian applications and they have also opened new avenues for Bayesian inference, first and foremost Bayesian model choice.

[1]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[2]  R. Tweedie,et al.  Rates of convergence of the Hastings and Metropolis algorithms , 1996 .

[3]  Tim Hesterberg,et al.  Monte Carlo Strategies in Scientific Computing , 2002, Technometrics.

[4]  G. Roberts,et al.  Bayesian inference for non‐Gaussian Ornstein–Uhlenbeck stochastic volatility processes , 2004 .

[5]  Christian P. Robert,et al.  Introducing Monte Carlo Methods with R , 2009 .

[6]  Jim Albert,et al.  Bayesian Computation with R , 2008 .

[7]  P. Moral,et al.  Sequential Monte Carlo samplers , 2002, cond-mat/0212648.

[8]  Xiao-Li Meng,et al.  SIMULATING RATIOS OF NORMALIZING CONSTANTS VIA A SIMPLE IDENTITY: A THEORETICAL EXPLORATION , 1996 .

[9]  James C. Spall,et al.  Introduction to stochastic search and optimization - estimation, simulation, and control , 2003, Wiley-Interscience series in discrete mathematics and optimization.

[10]  Tobias Rydén,et al.  Hidden Markov Models , 2006 .

[11]  C. Robert,et al.  Importance sampling methods for Bayesian discrimination between embedded models , 2009, 0910.2325.

[12]  R. Douc,et al.  Minimum variance importance sampling via Population Monte Carlo , 2007 .

[13]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[14]  C. Robert,et al.  Computational methods for Bayesian model choice , 2009, 0907.5123.

[15]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[16]  A. Owen,et al.  Safe and Effective Importance Sampling , 2000 .

[17]  D. Balding,et al.  Approximate Bayesian computation in population genetics. , 2002, Genetics.

[18]  Jean-Marie Cornuet,et al.  Adaptive Multiple Importance Sampling , 2009, 0907.1254.

[19]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[20]  Heikki Haario,et al.  Adaptive proposal distribution for random walk Metropolis algorithm , 1999, Comput. Stat..

[21]  Simon J. Godsill,et al.  Marginal maximum a posteriori estimation using Markov chain Monte Carlo , 2002, Stat. Comput..

[22]  J. Rosenthal,et al.  Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms , 2007, Journal of Applied Probability.

[23]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

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

[25]  P. Fearnhead,et al.  Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion) , 2006 .

[26]  C. Robert,et al.  Optimal Sample Size for Multiple Testing : the Case of Gene Expression Mi roarraysPeter , 2004 .

[27]  Christopher Holmes,et al.  Bayesian Methods for Nonlinear Classification and Regressing , 2002 .

[28]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[29]  W. Michael Conklin,et al.  Monte Carlo Methods in Bayesian Computation , 2001, Technometrics.

[30]  N. Metropolis.  THE BEGINNING of the MONTE CARLO METHOD , 2022 .

[31]  Eric Moulines,et al.  Stability of Stochastic Approximation under Verifiable Conditions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[32]  R. Douc,et al.  Convergence of Adaptive Sampling Schemes , 2007, 0708.0711.

[33]  Xiao-Li Meng,et al.  Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling , 1998 .

[34]  A. Graja.  Bayesian Analysis of Stochastic Volatility Models , 2009 .

[35]  Christian P. Robert,et al.  Bayesian computational methods , 2010, 1002.2702.

[36]  Refik Soyer,et al.  Bayesian Methods for Nonlinear Classification and Regression , 2004, Technometrics.

[37]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[38]  J. Bernardo,et al.  Simulation-Based Optimal Design , 1999 .

[39]  Colin Rose.  Computational Statistics , 2011, International Encyclopedia of Statistical Science.

[40]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[41]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[42]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[43]  Gersende Fort,et al.  Estimation of cosmological parameters using adaptive importance sampling , 2009, 0903.0837.

[44]  Jean-Michel Marin,et al.  Convergence of Adaptive Sampling Schemes , 2004 .

[45]  J. Marin,et al.  Population Monte Carlo , 2004 .

[46]  N. Shephard,et al.  Markov chain Monte Carlo methods for stochastic volatility models , 2002 .

[47]  S. Eddy.  Hidden Markov models. , 1996, Current opinion in structural biology.

[48]  Michael I. Jordan,et al.  Bayesian parameter estimation via variational methods , 2000, Stat. Comput..

[49]  D. Rubin.  Using the SIR algorithm to simulate posterior distributions , 1988 .

[50]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[51]  Jean-Michel Marin,et al.  Adaptive importance sampling in general mixture classes , 2007, Stat. Comput..

[52]  Yukito Iba,et al.  Population-based Monte Carlo algorithms , 2000 .

[53]  Gareth O. Roberts,et al.  Examples of Adaptive MCMC , 2009 .