Assessment and Adjustment of Approximate Inference Algorithms Using the Law of Total Variance

References

• Asmussen, S., and Rojas-Nandayapa, L. (2008), “Asymptotics of Sums of Lognormal Random Variables With Gaussian Copula,” Statistics and Probability Letters, 78, 2709–2714. DOI: 10.1016/j.spl.2008.03.035.
   Web of Science ®Google Scholar
• Beaumont, M. A., Zhang, W., and Balding, D. J. (2002), “Approximate Bayesian Computation in Population Genetics,” Genetics, 162, 2025–2035.
   PubMed Web of Science ®Google Scholar
• Blei, D. M., Kucukelbir, A., and McAuliffe, J. D. (2017), “Variational Inference: A Review for Statisticians,” Journal of the American Statistical Association, 112, 859–877. DOI: 10.1080/01621459.2017.1285773.
   Web of Science ®Google Scholar
• Blum, M. G. B. (2010), “Approximate Bayesian Computation: A Non-Parametric Perspective,” Journal of the American Statistical Association, 105, 1178–1187. DOI: 10.1198/jasa.2010.tm09448.
   Web of Science ®Google Scholar
• Blum, M. G. B., and François, O. (2010), “Non-Linear Regression Models for Approximate Bayesian Computation,” Statistics and Computing, 20, 63–75. DOI: 10.1007/s11222-009-9116-0.
   Web of Science ®Google Scholar
• Blum, M. G. B., Nunes, M. A., Prangle, D., and Sisson, S. A. (2013), “A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation,” Statistical Science, 28, 189–208. DOI: 10.1214/12-STS406.
   Web of Science ®Google Scholar
• Blum, M. G. B., and Tran, V. C. (2010), “HIV With Contact Tracing: A Case Study in Approximate Bayesian Computation,” Biostatistics, 11, 644–660. DOI: 10.1093/biostatistics/kxq022.
   PubMed Web of Science ®Google Scholar
• Brillinger, D. R. (1969), “The Calculation of Cumulants via Conditioning,” Annals of the Institute of Statistical Mathematics, 21, 215–218. DOI: 10.1007/BF02532246.
   Web of Science ®Google Scholar
• Chollet, F., and Allaire, J. J. (2018), Deep Learning With R (1st ed.), Greenwich, CT: Manning Publications Co.
   Google Scholar
• Chung, Y., Gelman, A., Rabe-Hesketh, S., Liu, J., and Dorie, V. (2015), “Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models,” Journal of Educational and Behavioral Statistics, 40, 136–157. DOI: 10.3102/1076998615570945.
   Web of Science ®Google Scholar
• Cook, S. R., Gelman, A., and Rubin, D. B. (2006), “Validation of Software for Bayesian Models Using Posterior Quantiles,” Journal of Computational and Graphical Statistics, 15, 675–692. DOI: 10.1198/106186006X136976.
   Web of Science ®Google Scholar
• Cressie, N., and Wikle, C. (2011), Statistics for Spatio-Temporal Data, New York: Wiley.
   Google Scholar
• Dey, K. K., and Bhattacharya, S. (2019), “A Brief Review of Optimal Scaling of the Main MCMC Approaches and Optimal Scaling of Additive TMCMC Under Non-Regular Cases,” Brazilian Journal of Probability and Statistics, 33, 222–266. DOI: 10.1214/17-BJPS386.
   Web of Science ®Google Scholar
• Dutta, S., and Bhattacharya, S. (2014), “Markov Chain Monte Carlo Based on Deterministic Transformations,” Statistical Methodology, 16, 100–116. DOI: 10.1016/j.stamet.2013.08.006.
   Google Scholar
• Fenton, L. (1960), “The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems,” IRE Transactions on Communications Systems, 8, 57–67. DOI: 10.1109/TCOM.1960.1097606.
   Google Scholar
• Frazier, D. T., Robert, C. P., and Rousseau, J. (2020), “Model Misspecification in Approximate Bayesian Computation: Consequences and Diagnostics,” Journal of the Royal Statistical Society, Series B, 82, 421–444. DOI: 10.1111/rssb.12356.
   Google Scholar
• Geil, P., Million, A., Rotte, R., and Zimmerman, K. F. (1997), “Economic Incentives and Hospitalization in Germany,” Journal of Applied Econometrics, 12, 295–311. DOI: 10.1002/(SICI)1099-1255(199705)12:3<295::AID-JAE443>3.0.CO;2-X.
   Web of Science ®Google Scholar
• Gelman, A. (2017), “Correction to Cook, Gelman, and Rubin (2006),” Journal of Computational and Graphical Statistics, 26, 940–940. DOI: 10.1080/10618600.2017.1377082.
   Web of Science ®Google Scholar
• Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A., and Rubin, D. (2013), Bayesian Data Analysis, Chapman & Hall/CRC Texts in Statistical Science (3rd ed.), Boca Raton, FL: CRC Press.
   Google Scholar
• Geweke, J. (2004), “Getting It Right: Joint Distribution Tests of Posterior Simulators,” Journal of the American Statistical Association, 99, 799–804. DOI: 10.1198/016214504000001132.
   Web of Science ®Google Scholar
• Giordano, R., Broderick, T., and Jordan, M. I. (2018), “Covariances, Robustness, and Variational Bayes,” Journal of Machine Learning Research, 19, 1–49.
   Web of Science ®Google Scholar
• Jaccard, P. (1901), “Étude comparative de la distribution florale dans une portion des Alpes et des Jura,” Bulletin de la Société vaudoise des sciences naturelles, 37, 547–579.
   Google Scholar
• Lee, J. E., Nicholls, G. K., and Ryder, R. J. (2019), “Calibration Procedures for Approximate Bayesian Credible Sets,” Bayesian Analysis, 14, 1245–1269. DOI: 10.1214/19-BA1175.
   Web of Science ®Google Scholar
• Li, J., Nott, D. J., Fan, Y., and Sisson, S. A. (2017), “Extending Approximate Bayesian Computation Methods to High Dimensions via Gaussian Copula,” Computational Statistics and Data Analysis, 106, 77–89. DOI: 10.1016/j.csda.2016.07.005.
   Web of Science ®Google Scholar
• MacDonald, B., Ranjan, P., and Chipman, H. (2015), “GPfit: An R Package for Fitting a Gaussian Process Model to Deterministic Simulator Outputs,” Journal of Statistical Software, 64, 1–23. DOI: 10.18637/jss.v064.i12.
   Web of Science ®Google Scholar
• Marin, J.-M., Pudlo, P., Robert, C. P., and Ryder, R. J. (2012), “Approximate Bayesian Computational Methods,” Statistics and Computing, 22, 1167–1180. DOI: 10.1007/s11222-011-9288-2.
   Web of Science ®Google Scholar
• Nott, D. J., Fan, Y., Marshall, L., and Sisson, S. A. (2014), “Approximate Bayesian Computation and Bayes Linear Analysis: Towards High-Dimensional ABC,” Journal of Computational and Graphical Statistics, 23, 65–86. DOI: 10.1080/10618600.2012.751874.
   Web of Science ®Google Scholar
• Ormerod, J. T., and Wand, M. P. (2010), “Explaining Variational Approximations,” The American Statistician, 64, 140–153. DOI: 10.1198/tast.2010.09058.
   Web of Science ®Google Scholar
• Prangle, D., Blum, M., Popovic, G., and Sisson, S. (2014), “Diagnostic Tools for Approximate Bayesian Computation Using the Coverage Property,” Australian & New Zealand Journal of Statistics, 56, 309– 329.
   Web of Science ®Google Scholar
• Rasmussen, C. E., and Williams, C. K. (2006), Gaussian Processes for Machine Learning, Cambridge, MA: The MIT Press.
   Google Scholar
• Raynal, L., Marin, J.-M., Pudlo, P., Ribatet, M., Robert, C. P., and Estoup, A. (2018), “ABC Random Forests for Bayesian Parameter Inference,” Bioinformatics, 35, 1720–1728. DOI: 10.1093/bioinformatics/bty867.
   Web of Science ®Google Scholar
• Rodrigues, G., Prangle, D., and Sisson, S. (2018), “Recalibration: A Post-Processing Method for Approximate Bayesian Computation,” Computational Statistics and Data Analysis, 126, 53–66. DOI: 10.1016/j.csda.2018.04.004.
   Web of Science ®Google Scholar
• Stan Development Team (2020), “RStan: The R Interface to Stan,” R Package Version 2.21.2.
   Google Scholar
• Talts, S., Betancourt, M., Simpson, D., Vehtari, A., and Gelman, A. (2018), “Validating Bayesian Inference Algorithms With Simulation-Based Calibration,” arXiv no. 1804.06788.
   Google Scholar
• Tran, M.-N., Nguyen, N., Nott, D., and Kohn, R. (2020), “Bayesian Deep Net GLM and GLMM,” Journal of Computational and Graphical Statistics, 29, 97–113. DOI: 10.1080/10618600.2019.1637747.
   Web of Science ®Google Scholar
• Wegmann, D., Leuenberger, C., and Excoffier, L. (2009), “Efficient Approximate Bayesian Computation Coupled With Markov Chain Monte Carlo Without Likelihood,” Genetics, 182, 1207–1218. DOI: 10.1534/genetics.109.102509.
   PubMed Web of Science ®Google Scholar
• Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2018), “Yes, But Did It Work? Evaluating Variational Inference,” in Proceedings of Machine Learning Research, Stockholmsmssan, Stockholm, Sweden, PMLR (Vol. 80), pp. 5581–5590.
   Google Scholar