Convergence of Griddy Gibbs sampling and other perturbed Markov chains

References

• Ritter C, Tanner MA. Facilitating the Gibbs Sampler: the Gibbs Stopper and the Griddy-Gibbs Sampler. J Am Stat Assoc. 1992;87(419):861–868. doi: 10.1080/01621459.1992.10475289
   Web of Science ®Google Scholar
• Ray B, McCulloch R, Tsa R. Bayesian methods for change-point detection in long-range dependent processes. Stat Sin. 1997;7:451–472.
   Google Scholar
• Barnard J, McCulloch R, Meng X. Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Stat Sin. 2000;10:1281–1311.
   Web of Science ®Google Scholar
• Yang H, Liu F, Ji C, et al. Adaptive sampling for Bayesian geospatial models. Statist Comput. 2014;24(6):1101–1110. doi: 10.1007/s11222-013-9422-4
   Web of Science ®Google Scholar
• Kundu S, David BD. Bayes variable selection in semiparametric linear models. J Am Stat Assoc. 2014;109(505):437–447. doi: 10.1080/01621459.2014.881153
   PubMed Web of Science ®Google Scholar
• Kundu S, David BD. Latent factor models for density estimation. Biometrika. 2014;101(3):641–654. doi: 10.1093/biomet/asu019
   Web of Science ®Google Scholar
• Pham TH, Ormerod JT, Wand MP. Mean field variational Bayesian inference for nonparametric regression with measurement error. Comput Stat Data Anal. 2013;68:375–387. doi: 10.1016/j.csda.2013.07.014
   Web of Science ®Google Scholar
• Mansinghka V, Kulkarni TD, Perov YN, et al. Approximate Bayesian image interpretation using generative probabilistic graphics programs. Adv Neural Inf Process Syst. 2013;26:1520–1528.
   Google Scholar
• Ritter C. Statistical analysis of spectra from electron spectroscopy for chemical analysis. J R Stat Soc D – Stat. 1994;43:111–127.
   Google Scholar
• Dong W, Tang X, Yu Y, et al. Systems biology of the clock in Neurospora crassa. PLoS ONE. 2008;3(8):e3105. doi: 10.1371/journal.pone.0003105
   PubMed Web of Science ®Google Scholar
• Dinh V, Rundell AE, Buzzard GT. Experimental design for dynamics identification of cellular processes. Bull Math Biol. 2014;76(3):597–626. doi: 10.1007/s11538-014-9935-9
   PubMed Web of Science ®Google Scholar
• Dinh V, Rundell AE, Buzzard GT. Effective sampling schemes for behavior discrimination in nonlinear systems. Int J Uncertain Quantification. 2014;4(6):535–554. doi: 10.1615/Int.J.UncertaintyQuantification.2014010728
   Web of Science ®Google Scholar
• Li J, Yang X, Shoptaw S. A random-effects Markov transition model for Poisson-distributed repeated measures with non-ignorable missing values. Stat Med. 2007;26(12):2519–2532. doi: 10.1002/sim.2717
   PubMed Web of Science ®Google Scholar
• Ardia D, Hoogerheide L, Dijk H. Adaptive mixture of Student-t distributions as a flexible candidate distribution for efficient simulation: the R Package AdMit. J Stat Softw. 2009;29:1–32. doi: 10.18637/jss.v029.i03
   Web of Science ®Google Scholar
• Ausna M, Galeano P. Bayesian estimation of the Gaussian mixture GARCH model. Comput Stat Data Anal. 2007;51(5):2636–2652. doi: 10.1016/j.csda.2006.01.006
   Web of Science ®Google Scholar
• Boatwright P, McCulloch R, Rossi P. Account-level modeling for trade promotion: an application of a constrained parameter hierarchical model. J Am Stat Assoc. 1999;94(448):1063–1073. doi: 10.1080/01621459.1999.10473859
   Web of Science ®Google Scholar
• Bauwens L, Rombouts J. Bayesian inference for the mixed conditional heteroskedasticity model. Economet J. 2007;10(2):408–425. doi: 10.1111/j.1368-423X.2007.00213.x
   Web of Science ®Google Scholar
• Walkera D, Prez Barberab F, Marion G. Stochastic modelling of ecological processes using hybrid Gibbs samplers. Ecol Model. 2006;198(1/2):40–52. doi: 10.1016/j.ecolmodel.2006.04.008
   Web of Science ®Google Scholar
• Bauwens L, Rombouts J. Bayesian clustering of many GARCH models. Economet Rev. 2007;26(2–4):365–386. doi: 10.1080/07474930701220576
   Web of Science ®Google Scholar
• Michalopoulou Z, Picarelli M. Gibbs sampling for time-delay and amplitude estimation in underwater acoustics. J Acoust Soc Am. 2005;117(2):799–8087. doi: 10.1121/1.1847894
   PubMed Web of Science ®Google Scholar
• Boatwright P, McCulloch R, Rossi P. A multivariate time series model for the analysis and prediction of carbon monoxide atmospheric concentrations. J R Stat Soc C – Appl. 2001;50(2):187–200. doi: 10.1111/1467-9876.00228
   Web of Science ®Google Scholar
• Ray B, Tsa R. Bayesian methods for change-point detection in long-range dependent processes. J Time Ser Anal. 2002;23(6):687–705. doi: 10.1111/1467-9892.00286
   Web of Science ®Google Scholar
• Chen C, Wen Y. On goodness of fit for time series regression models. J Stat Comput Simul. 2001;69(3):239–256. doi: 10.1080/00949650108812093
   Web of Science ®Google Scholar
• Tierney L. Markov chains for exploring posterior distributions. Ann Stat. 1994;22(4):1701–1728. doi: 10.1214/aos/1176325750
   Web of Science ®Google Scholar
• Liu SJ, Liang F, Wong WH. The multiple-try method and local optimization in metropolis sampling. J Am Stat Assoc. 95(449):121–134. doi: 10.1080/01621459.2000.10473908
   Web of Science ®Google Scholar
• Gilks WR, Wild P. Adaptive rejection sampling for Gibbs sampling. Appl Stat. 1992;1(2):337–48. doi: 10.2307/2347565
   Web of Science ®Google Scholar
• Roberts GO, Rosenthal JS, Schwartz PO. Convergence properties of perturbed Markov chains. J Appl Probab. 1998;35(1):1–11. doi: 10.1017/S0021900200014625
   Web of Science ®Google Scholar
• Mitrophanov AY. Sensitivity and convergence of uniformly ergodic Markov chains. J Appl Probab. 2005;42(04):1003–1014. doi: 10.1017/S0021900200001066
   Google Scholar
• Andrieu C, Roberts GO. The pseudo-marginal approach for efficient Monte Carlo computations. Ann Stat. 2009;37(2):697–725. doi: 10.1214/07-AOS574
   Web of Science ®Google Scholar
• Roberts GO, Rosenthal JS. General state space Markov chains and MCMC algorithms. Probab Surv. 2004;1:20–71. doi: 10.1214/154957804100000024
   Google Scholar
• Athreya K, Doss H, Sethuraman J. On the convergence of the Markov Chain simulation method. Ann Stat. 1996;24(1):69–100. doi: 10.1214/aos/1033066200
   Web of Science ®Google Scholar
• Koralov L, Sinai Y. Theory of probability and random processes. Berlin: Springer; 2007.
   Google Scholar
• Pedersen M. Functional analysis in applied mathematics and engineering. Boca Raton (FL): CRC Press; 1999.
   Google Scholar
• Lasser R. Introduction to Fourier analysis. New York (NY): CRC Press; 1996.
   Google Scholar
• Lillacci G, Khammash G. A distribution-matching method for parameter estimation and model selection in computational biology. Int J Robust Nonlinear Control. 2012;22(10):1065–1081. doi: 10.1002/rnc.2794
   Web of Science ®Google Scholar
• Lipniacki T, Hat B, Faeder JR, et al. Stochastic effects and bistability in T cell receptor signaling. J Theoret Biol. 2008;254(1):110–122. doi: 10.1016/j.jtbi.2008.05.001
   PubMed Web of Science ®Google Scholar
• Donahue MM, Buzzard GT, Rundell AE. Experiment design through dynamical characterisation of non-linear systems biology models utilising sparse grids. IET Syst Biol. 2010;4(4):249–262. doi: 10.1049/iet-syb.2009.0031
   PubMed Web of Science ®Google Scholar
• Buzzard GT. Global sensitivity analysis using sparse grid interpolation and polynomial chaos. Reliab Eng Syst Saf. 2012;17:82–89. doi: 10.1016/j.ress.2011.07.011
   Web of Science ®Google Scholar