The Data Augmentation Algorithm: Theory and Methodology

[1]  R. Tweedie,et al.  Geometric L 2 and L 1 convergence are equivalent for reversible Markov chains , 2001, Journal of Applied Probability.

[2]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

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

[4]  Jeffrey S. Rosenthal,et al.  Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms , 2003 .

[5]  E. Nummelin General irreducible Markov chains and non-negative operators: Notes and comments , 1984 .

[6]  Xiao-Li Meng,et al.  The Art of Data Augmentation , 2001 .

[7]  J. Rosenthal,et al.  General state space Markov chains and MCMC algorithms , 2004, math/0404033.

[8]  Michael W Deem,et al.  Parallel tempering: theory, applications, and new perspectives. , 2005, Physical chemistry chemical physics : PCCP.

[9]  Jun S. Liu,et al.  Covariance Structure and Convergence Rate of the Gibbs Sampler with Various Scans , 1995 .

[10]  Gareth O. Roberts,et al.  Markov Chains and De‐initializing Processes , 2001 .

[11]  J. Hobert,et al.  Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression , 2007 .

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

[13]  Galin L. Jones,et al.  Fixed-Width Output Analysis for Markov Chain Monte Carlo , 2006, math/0601446.

[14]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[15]  Murali Haran,et al.  Markov chain Monte Carlo: Can we trust the third significant figure? , 2007, math/0703746.

[16]  J. Hobert,et al.  Block Gibbs Sampling for Bayesian Random Effects Models With Improper Priors: Convergence and Regeneration , 2009 .

[17]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[18]  J. Geweke,et al.  Bayesian Inference in Econometric Models Using Monte Carlo Integration , 1989 .

[19]  Xiao-Li Meng,et al.  Seeking efficient data augmentation schemes via conditional and marginal augmentation , 1999 .

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

[21]  Jun S. Liu,et al.  Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes , 1994 .

[22]  J. Hobert,et al.  Geometric Ergodicity of van Dyk and Meng's Algorithm for the Multivariate Student's t Model , 2004 .

[23]  J. Hobert,et al.  A theoretical comparison of the data augmentation, marginal augmentation and PX-DA algorithms , 2008, 0804.0671.

[24]  Adrian F. M. Smith,et al.  Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms , 1994 .

[25]  C. Geyer,et al.  Discussion: Markov Chains for Exploring Posterior Distributions , 1994 .

[26]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[27]  James Allen Fill,et al.  Extension of Fill's perfect rejection sampling algorithm to general chains (Extended abstract) , 2000 .

[28]  C. Robert Simulation of truncated normal variables , 2009, 0907.4010.

[29]  Bin Yu,et al.  Regeneration in Markov chain samplers , 1995 .

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

[31]  P. Green Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[32]  James P. Hobert,et al.  Norm Comparisons for Data Augmentation , 2007 .

[33]  P. Diaconis,et al.  Geometric Bounds for Eigenvalues of Markov Chains , 1991 .

[34]  M. L. Eaton Group invariance applications in statistics , 1989 .

[35]  M. Steel,et al.  Multivariate Student -t Regression Models : Pitfalls and Inference , 1999 .

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

[37]  J. Rosenthal,et al.  Geometric Ergodicity and Hybrid Markov Chains , 1997 .

[38]  P. Diaconis,et al.  Gibbs sampling, exponential families and orthogonal polynomials , 2008, 0808.3852.

[39]  J. Rosenthal,et al.  Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains , 2006, math/0702412.

[40]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[41]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[42]  Galin L. Jones,et al.  On the applicability of regenerative simulation in Markov chain Monte Carlo , 2002 .

[43]  Ming-Hui Chen,et al.  Propriety of posterior distribution for dichotomous quantal response models , 2000 .

[44]  G. Torrie,et al.  Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling , 1977 .

[45]  S. Walker Invited comment on the paper "Slice Sampling" by Radford Neal , 2003 .

[46]  Ruitao Liu,et al.  When is Eaton’s Markov chain irreducible? , 2007 .

[47]  G. Parisi,et al.  Simulated tempering: a new Monte Carlo scheme , 1992, hep-lat/9205018.

[48]  Jun S. Liu,et al.  Parameter Expansion for Data Augmentation , 1999 .