References

[1]D Allingham, RA King, and KL Mengersen. Bayesian estimation of quantile distributions. Statistics and Computing, 19(2):189–201, 2009.
[2]D Bates, J M White, J Bezanson, S Karpinski, V B Shah, and other contributors. Distributions. 2014. julia software package. URL: https://github.com/JuliaStats/Distributions.jl.
[3]J Bezanson, S Karpinski, V B Shah, and A Edelman. Julia: a fast dynamic language for technical computing. arXiv:1209.5145 [cs.PL], 2012. URL: http://arxiv.org/abs/1209.5145.
[4]J Bezanson, S Karpinski, V B Shah, and other contributors. The Julia Language. 2014. URL: http://julialang.org/.
[5]D Birkes and Y Dodge, editors. Alternative Methods of Regression. Wiley, New York, 1993.
[6]R D Boch and M Lieberman. Fitting a response model for n dichotomously scored items. Psychometrika, 35:179–197, 1970.
[7]J K Bowmaker, G H Jacobs, D J Spiegelhalter, and J D Mollon. Two types of trichromatic squirrel monkey share a pigment in the red-green region. Vision Research, 25:1937–1946, 1985.
[8]G E Box and G C Tiao, editors. Bayesian Inference in Statistical Analysis. Addison Wesley, Reading, MA, 1973.
[9]N E Breslow. Extra-Poisson variation in log-linear models. Applied Statistics, 33:38–44, 1984.
[10]N E Breslow and D G Clayton. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88:9–25, 1993.
[11]S Brooks and A Gelman. General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7(4):434–455, 1998.
[12]S Brooks, A Gelman, G L Jones, and X-L Meng, editors. Handbook of Markov Chain Monte Carlo. Chapman & Hall/CRC, Boca Raton, FL, 2011.
[13]K A Brownlee, editor. Statistical Theory and Methodology in Science and Engineering. Wiley, New York, 1965.
[14]J B Carlin. Meta-analysis for 2 x 2 tables: a Bayesian approach. Statistics in Medicine, 11:141–159, 1992.
[15]M-H Chen and Q-M Shao. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1):69–92, 1999.
[16]D Clayton. Bayesian analysis of frailty models. Technical Report, Medical Research Council Biostatistics Unit, Cambridge, 1994.
[17]M K Cowles and B P Carlin. Markov chain Monte Carlo convergence diagnostics: a comparative review. Journal of the American Statistical Association, 91:883–904, 1996.
[18]M K Cowles, J Yan, and B J Smith. Reparameterized and marginalized posterior and predictive sampling for complex Bayesian geostatistical models. Journal of Computational and Graphical Statistics, 2:262–282, 2009.
[19]M Crowder. Beta-Binomial ANOVA for proportions. Applied Statistics, 27:34–37, 1978.
[20]O L Davies. Statistical Methods in Research and Production. Olver & Boyd, Edinburgh and London, 1967.
[21]P Dellaportas and A F M Smith. Bayesian inference for generalized linear and proportional hazards model via Gibbs sampling. Applied Statistics, 42:443–460, 1993.
[22]S Duane, A D Kennedy, B J Pendleton, and D Roweth. Higher order hybrid Monte Carlo algorithms. Physics Letters B, 195:216–222, 1987.
[23]R C Elston and J E Grizzle. Estimation of time-response curves and their confidence bounds. Biometrics, 18:148–159, 1962.
[24]F Ezzet and J Whitehead. A random effects model for ordinal responses from a crossover trial. Statistics in Medicine, 10:901–907, 1993.
[25]Keno Fischer and other contributors. GraphViz. 2014. julia software package. URL: https://github.com/Keno/GraphViz.jl.
[26]E Frierich and E Gehan. The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukaemia: a model for evaluation of other potentially useful therapy. Blood, 21:699–716, 1963.
[27]D Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman & Hall/CRC, Boca Raton, FL, 1997.
[28]A E Gelfand, S Hills, A Racine-Poon, and A F M Smith. Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association, 85:972–985, 1990.
[29]A E Gelfand and A F M Smith. Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85:398–409, 1990.
[30]A Gelman, J B Carlin, H S Stern, D B Dunson, A V Vehtari, and Rubin D B. Bayesian Data Analysis: Third Edition. CRC Press, 2013.
[31]A Gelman, G O Roberts, and W R Gilks. Efficient Metropolis jumping rules. Bayesian Statistics, 5:599–607, 1996.
[32]A Gelman and D B Rubin. Inference from iterative simulation using multiple sequences. Statistical Science, 7:457–511, 1992.
[33]A Gelman, Y-S Su, M Yajima, J Hill, M G Pittau, J Kerman, T Zheng, and V Dorie. arm: Data Analysis Using Regression and Multilevel/Hierarchical Models. 2014. R software package. URL: http://CRAN.R-project.org/package=arm.
[34]S Geman and D Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6):721–741, 1984.
[35]E I George, U E Makov, and A F M Smith. Conjugate likelihood distributions. Scandinavian Journal of Statistics, 20:147–156, 1993.
[36]J Geweke. Bayesian Statistics., chapter Evaluating the Accuracy of Sampling-Based Approaches to Calculating Posterior Moments. volume 4. Oxford University Press, New York, 1992.
[37]C J Geyer. Practical Markov chain Monte Carlo. Statistical Science, 7:473–511, 1992.
[38]W R Gilks, S Richardson, and D J Spiegelhalter, editors. Monte Carlo in Practice. Chapman & Hall/CRC, Boca Raton, FL, 1996.
[39]M Girolami and B Calderhead. Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society: Series B, 73(2):123–214, 2011.
[40]P W Glynn and W Whitt. Estimating the asymptotic variance with batch means. Operations Research Letters, 10:431–435, 1991.
[41]A P Grieve. Applications of Bayesian software: two examples. Statistician, 36:283–288, 1987.
[42]OpenBUGS Project Management Group. OpenBUGS Examples. 2014. version 3.2.3. URL: http://www.openbugs.net/w/Examples.
[43]H Haario, E Saksman, and J Tamminen. An adaptive Metropolis algorithm. Bernoulli, 7:223–242, 2001.
[44]W K Hastings. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1):97–109, 1970.
[45]P Heidelberger and P Welch. Simulation run length control in the presence of an initial transient. Operations Research, 31:1109–1144, 1983.
[46]M D Hoffman and A Gelman. The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15:1593–1623, 2014. URL: http://jmlr.org/papers/v15/hoffman14a.html.
[47]SAS Institute Inc. The MCMC Procedure. SAS Institute Inc., Cary, NC, 2015.
[48]Steven G Johnson, Fernando Perez, Jeff Bezanson, Stefan Karpinski, Keno Fischer, and other contributors. IJulia. 2015. julia software package. URL: https://github.com/JuliaLang/IJulia.jl.
[49]D C Jones. Gadfly. 2014. julia software package. URL: https://github.com/dcjones/Gadfly.jl.
[50]J G Kalbfleisch. Probability and Statistical Inference: Volume 2. Springer-Verlag, New York, 1985.
[51]D Lin, S Byrne, A N Jensen, D Bates, J M White, S Kornblith, and other contributors. StatsBase. 2014. julia software package. URL: https://github.com/JuliaStats/StatsBase.jl.
[52]D V Lindley and A F M Smith. Bayes estimates for the linear model (with discussion). Journal of the Royal Statistical Society: Series B, 34:1–44, 1972.
[53]J S Liu. Peskun’s Theorem and a modified discrete-state Gibbs sampler. Biometrika, 83(3):681–682, 1996.
[54]D Lunn, C Jackons, N Best, Thomas A,, and D Spiegelhalter. The BUGS Book: A Practical Introduction to Bayesian Analysis. Chapman & Hall/CRC, Boca Raton, FL, 2012.
[55]D Lunn, D Spiegelhalter, A Thomas, and N Best. The BUGS project: evolution, critique and future directions. Statistics in Medicine, 28(25):3049–3067, 2009.
[56]D Madigan, J York, and D Allard. Bayesian graphical models for discrete data. Revue Internationale de Statistique, 63(2):215–232, 1995.
[57]P Marjoram, J Molitor, V Plagnol, and S Tavaré. Markov chain Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences of the United States of America, 100(26):15324–15328, 2003.
[58]A D Martin, K M Quinn, and J H Park. MCMCpack: Markov Chain Monte Carlo (MCMC) Package. 2013. R software package. URL: http://CRAN.R-project.org/package=MCMCpack.
[59]G C McDonald and R C Schwing. Instabilities of regression estimates relating air pollution to mortality. Technometrics, 15(3):463–481, 1973.
[60]C McGilchrist and C Aisbett. Regression with frailty in survival analysis. Biometrics, 47:461–466, 1991.
[61]N Metropolis, A W Rosenbluth, M N Rosenbluth, A H Teller, and E Teller. Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21(6):1087–1092, 1953.
[62]R M Neal. Slice sampling (with discussion). Annals of Statistics, 31:705–767, 2003.
[63]R M Neal. Handbook of Markov Chain Monte Carlo., chapter MCMC Using Hamiltonian Dynamics, pages 113–162. CRC Press, 2011.
[64]R M Neal. GRIMS – general R interface for Markov sampling. 2012. [Online; accessed 5-March-2014]. URL: http://www.cs.toronto.edu/~radford/GRIMS.html.
[65]R B O’Hara and M J Sillanpää. A review of Bayesian variable selection methods: what, how and which. Bayesian Analysis, 4(1):85–117, 2009.
[66]A Pakman and L Paninski. Auxiliary-variable exact Hamiltonian Monte Carlo samplers for binary distributions. In C.j.c. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.q. Weinberger, editors, Advances in Neural Information Processing Systems 26, pages 2409–2498. 2013. URL: http://media.nips.cc/nipsbooks/nipspapers/paper_files/nips26/1176.pdf.
[67]J H Park. CRAN Task View: Bayesian Inference. 2014. version 2014-05-16. URL: http://cran.r-project.org/web/views/Bayesian.html.
[68]A Patil, D Huard, and C J Fonnesbeck. PyMC: Bayesian stochastic modelling in Python. Journal of Statistical Software, 35(4):1–81, 2010.
[69]M Plummer. JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003). Vienna, Austria, March 20–22 2003. ISSN 1609-395X.
[70]M Plummer, N Best, K Cowles, and K Vines. CODA: convergence diagnosis and output analysis for MCMC. R News, 6(1):7–11, 2006.
[71]M Plummer, N Best, K Cowles, K Vines, D Sarkar, and R Almond. coda: Output Analysis and Diagnostics for MCMC. 2012. R software package. URL: http://CRAN.R-project.org/package=coda.
[72]A L Raftery and S Lewis. Comment: One long run with diagnostics: implementation strategies for Markov chain Monte Carlo. Statistical Science, 7(4):493–497, 1992.
[73]A L Raftery and S Lewis. Bayesian Statistics., chapter How Many Iterations in the Gibbs Sampler? volume 4. Oxford University Press, New York, 1992.
[74]GD Rayner and HL MacGillivray. Numerical maximum likelihood estimation for the g-and-k and generalized g-and-h distributions. Statistics and Computing, 12(1):57–75, 2002.
[75]C Robert. Markov chain Monte Carlo in practice., chapter Mixtures of distributions: inference and estimation. Chapman & Hall, 1994.
[76]C Robert and G Casella. Monte Carlo Statistical Methods. Springer, New York, 2nd edition, 2004.
[77]G O Roberts and J S Rosenthal. Examples of adaptive MCMC. Journal of Computational and Graphical Statistics, 18(2):349–367, 2009.
[78]G O Roberts and O Stramer. Langevin diffusions and Metropolis-Hastings algorithms. Methodology and Computing in Applied Probability, 4(4):337–357, 2002.
[79]G O Roberts and R L Tweedie. Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli, 2(4):341–363, 1996.
[80]A F Roche, H Wainer, and D Thissen. Skeletal maturity: The knee joint as a biological indicator. Plenum, New York, 1975.
[81]C A Schäfer. Monte Carlo Methods for Sampling High-Dimensional Binary Vectors. PhD thesis, Université Paris-Dauphine, 2012.
[82]C A Schäfer and N Chopin. Sequential Monte Carlo on large binary sampling spaces. Statistics and Computing, 23(2):163–184, 2013.
[83]S A Sisson and Y Fan. Handbook of Markov Chain Monte Carlo., chapter Likelihood-Free MCMC, pages 313–335. CRC Press, 2011.
[84]B J Smith. boa: an R package for MCMC output convergence assessment and posterior inference. Journal of Statistical Computing, 21(11):1–37, 2007.
[85]B J Smith. boa: Bayesian Output Analysis Program for MCMC. 2008. R software package. URL: http://CRAN.R-project.org/package=boa.
[86]B J Smith and other contributors. Mamba: Markov Chain Monte Carlo for Bayesian Analysis in julia. 2014. julia software package. URL: https://github.com/brian-j-smith/Mamba.jl.
[87]D Spiegelhalter, A Thomas, N Best, and W Gilks. BUGS 0.5 Bayesian Inference Using Gibbs Sampling Manual (version ii). MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK, August 1996.
[88]D Spiegelhalter, A Thomas, N Best, and D Lunn. OpenBUGS User Manual. March 2014. version 3.2.3. URL: http://www.openbugs.net/Manuals/Manual.html.
[89]D J Spiegelhalter, N G Best, B P Carlin, and A van der Linde. Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B, 64(4):583–639, 2002.
[90]P F Thall and S C Vail. Some covariance models for longitudinal count data with overdispersion. Biometrics, 46:657–671, 1990.
[91]D Thissen. MULITLOG Version 5: User’s Guide. Scientific Software, Mooresville, IN, 5th edition, 1986.
[92]A Thomas. OpenBUGS Developer Manual. March 2014. version 3.2.3. URL: http://www.openbugs.net/Manuals/Developer/Manual.html.
[93]L Tierney. Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22:1701–1762, 1994.
[94]D Wabersich and J Vandekerckhove. Extending JAGS: a tutorial on adding custom distributions to JAGS (with a diffusion model example). Behavior Research Methods, 2013. DOI 10.3758/s13428-013-0369-3.
[95]J M White and other contributors. Calculus. 2014. julia software package. URL: https://github.com/johnmyleswhite/Calculus.jl.
[96]J M White and other contributors. Graphs. 2014. julia software package. URL: https://github.com/JuliaLang/Graphs.jl.
[97]Stan Development Team. Stan: a C++ library for probability and sampling. 2014. URL: http://mc-stan.org/.
[98]Statisticat, LLC. LaplacesDemon: Complete Environment for Bayesian Inference. 2014. R software package. URL: http://www.bayesian-inference.com/software.