Bayesian Inference on High-Dimensional Multivariate Binary Responses

References

• Amemiya, T. (1985), Advanced Econometrics, Cambridge, MA: Harvard University Press.
   Google Scholar
• Ashford, J., and Sowden, R. (1970), “Multi-Variate Probit Analysis,” Biometrics, 26, 535–546.
   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
• Bock, R. D., and Gibbons, R. D. (1996), “High-Dimensional Multivariate Probit Analysis,” Biometrics, 52, 1183–1194.
   PubMed Web of Science ®Google Scholar
• Botev, Z. I. (2017), “The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting,” Journal of the Royal Statistical Society, Series B, 79, 125–148. DOI: 10.1111/rssb.12162.
   Google Scholar
• Chen, D., Xue, Y., and Gomes, C. (2018), “End-to-End Learning for the Deep Multivariate Probit Model,” in International Conference on Machine Learning, pp. 932–941, PMLR.
   Google Scholar
• Chib, S., and Greenberg, E. (1998), “Analysis of Multivariate Probit Models,” Biometrika, 85, 347–361. DOI: 10.1093/biomet/85.2.347.
   Web of Science ®Google Scholar
• Cox, D. R. (1972), “The Analysis of Multivariate Binary Data,” Journal of the Royal Statistical Society, Series C, 21, 113–120. DOI: 10.2307/2346482.
   Web of Science ®Google Scholar
• Davenport, C. A., Maity, A., Sullivan, P. F., and Tzeng, J.-Y. (2018), “A Powerful Test for snp Effects on Multivariate Binary Outcomes Using Kernel Machine Regression,” Statistics in Biosciences, 10, 117–138. DOI: 10.1007/s12561-017-9189-9.
   PubMed Web of Science ®Google Scholar
• Geisser, S., Hodges, J., Press, S., and ZeUner, A. (1990), “The Validity of Posterior Expansions based on Laplace’s Method,” Bayesian and Likelihood Methods in Statistics and Econometrics, 7, 473–488.
   Google Scholar
• Hardin, J. W. (2002), “The Robust Variance Estimator for Two-Stage Models,” The Stata Journal, 2, 253–266. DOI: 10.1177/1536867X0200200302.
   Web of Science ®Google Scholar
• Huang, A., and Wand, M. P. (2013), “Simple Marginally Noninformative Prior Distributions for Covariance Matrices,” Bayesian Analysis, 8, 439–452. DOI: 10.1214/13-BA815.
   Web of Science ®Google Scholar
• Joe, H. (2005), “Asymptotic Efficiency of the Two-Stage Estimation Method for Copula-based Models,” Journal of Multivariate Analysis, 94, 401–419. DOI: 10.1016/j.jmva.2004.06.003.
   Web of Science ®Google Scholar
• Johndrow, J. E., Smith, A., Pillai, N., and Dunson, D. B. (2019), “MCMC for Imbalanced Categorical Data,” Journal of the American Statistical Association, 114, 1394–1403. DOI: 10.1080/01621459.2018.1505626.
   Web of Science ®Google Scholar
• Ko, V., and Hjort, N. L. (2019), “Model Robust Inference with Two-Stage Maximum Likelihood Estimation for Copulas,” Journal of Multivariate Analysis, 171, 362–381. DOI: 10.1016/j.jmva.2019.01.004.
   Web of Science ®Google Scholar
• Lee, S., Huang, J. Z., and Hu, J. (2010), “Sparse Logistic Principal Components Analysis for Binary Data,” The Annals of Applied Statistics, 4, 1579–1601. DOI: 10.1214/10-AOAS327.
   PubMed Web of Science ®Google Scholar
• Lewandowski, D., Kurowicka, D., and Joe, H. (2009), “Generating Random Correlation Matrices based on Vines and Extended Onion Method,” Journal of Multivariate Analysis, 100, 1989–2001. DOI: 10.1016/j.jmva.2009.04.008.
   Web of Science ®Google Scholar
• Lindsay, B. G. (1988), “Composite Likelihood Methods,” Contemporary Mathematics, 80, 221–239.
   Google Scholar
• Lindström, Å., Green, M., Husby, M., Kålås, J. A., and Lehikoinen, A. (2015), “Large-Scale Monitoring of Waders on their Boreal and Arctic Breeding Grounds in Northern Europe,” Ardea, 103, 3–15. DOI: 10.5253/arde.v103i1.a1.
   Web of Science ®Google Scholar
• Miller, J. W. (2021), “Asymptotic Normality, Concentration, and Coverage of Generalized Posteriors,” Journal of Machine Learning Research, 22, 1–53.
   Web of Science ®Google Scholar
• Murphy, K. M., and Topel, R. H. (2002), “Estimation and Inference in Two-Step Econometric Models,” Journal of Business & Economic Statistics, 20, 88–97. DOI: 10.1198/073500102753410417.
   Web of Science ®Google Scholar
• Niittynen, P., and Luoto, M. (2018), “The Importance of Snow in Species Distribution Models of Arctic Vegetation,” Ecography, 41, 1024–1037. DOI: 10.1111/ecog.03348.
   Web of Science ®Google Scholar
• Norberg, A., Abrego, N., Blanchet, F. G., Adler, F. R., Anderson, B. J., Anttila, J., Araújo, M. B., Dallas, T., Dunson, D., Elith, J., et al. (2019), “A Comprehensive Evaluation of Predictive Performance of 33 Species Distribution Models at Species and Community Levels,” Ecological Monographs, 89, e01370. DOI: 10.1002/ecm.1370.
   Web of Science ®Google Scholar
• Ovaskainen, O., Tikhonov, G., Norberg, A., Guillaume Blanchet, F., Duan, L., Dunson, D., Roslin, T., and Abrego, N. (2017), “How to Make More Out of Community Data? A Conceptual Framework and its Implementation as Models and Software,” Ecology Letters, 20, 561–576. DOI: 10.1111/ele.12757.
   PubMed Web of Science ®Google Scholar
• Pakman, A., and Paninski, L. (2014), “Exact Hamiltonian Monte Carlo for Truncated Multivariate Gaussians,” Journal of Computational and Graphical Statistics, 23, 518–542. DOI: 10.1080/10618600.2013.788448.
   Web of Science ®Google Scholar
• Pichler, M., and Hartig, F. (2020), “A New Method for Faster and More Accurate Inference of Species Associations from Novel Community Data,” arXiv preprint arXiv:2003.05331.
   Google Scholar
• Rue, H., Martino, S., and Chopin, N. (2009), “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations,” Journal of the Royal Statistical Society, Series B, 71, 319–392. DOI: 10.1111/j.1467-9868.2008.00700.x.
   Web of Science ®Google Scholar
• Shih, J. H., and Louis, T. A. (1995), “Inferences on the Association Parameter in Copula Models for Bivariate Survival Data,” Biometrics, 51,1384–1399.
   PubMed Web of Science ®Google Scholar
• Stan Development Team. (2021), RStan: the R interface to Stan. R package version 2.21.3.
   Google Scholar
• Tierney, L., and Kadane, J. B. (1986), “Accurate Approximations for Posterior Moments and Marginal Densities,” Journal of the American Statistical Association, 81, 82–86. DOI: 10.1080/01621459.1986.10478240.
   Web of Science ®Google Scholar
• Ting, B., Wright, F., and Zhou, Y.-H. (2022), “Fast Multivariate Probit Estimation via a Two-Stage Composite Likelihood,” Statistics in Biosciences, 14, 533–549. DOI: 10.1007/s12561-022-09338-6.
   Web of Science ®Google Scholar
• Van der Vaart, A. W. (2000), Asymptotic Statistics (Vol. 3), Cambridge: Cambridge University Press.
   Google Scholar
• Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
   Web of Science ®Google Scholar
• Warton, D. I., Blanchet, F. G., O’Hara, R. B., Ovaskainen, O., Taskinen, S., Walker, S. C., and Hui, F. K. (2015), “So Many Variables: Joint Modeling in Community Ecology,” Trends in Ecology & Evolution, 30, 766–779. DOI: 10.1016/j.tree.2015.09.007.
   PubMed Web of Science ®Google Scholar
• Yi, G. Y., Zeng, L., and Cook, R. J. (2011), “A Robust Pairwise Likelihood Method for Incomplete Longitudinal Binary Data Arising in Clusters,” Canadian Journal of Statistics, 39, 34–51. DOI: 10.1002/cjs.10089.
   Web of Science ®Google Scholar
• Zhang, Z., Nishimura, A., Bastide, P., Ji, X., Payne, R. P., Goulder, P., Lemey, P., and Suchard, M. A. (2021), “Large-Scale Inference of Correlation Among Mixed-Type Biological Traits with Phylogenetic Multivariate Probit Models,” The Annals of Applied Statistics, 15, 230–251. DOI: 10.1214/20-AOAS1394.
   Web of Science ®Google Scholar
• Zhao, X., Plata, G., and Dixit, P. D. (2021), “Sigmoid: A Super-Statistical Generative Model for Binary Data,” PLOS Computational Biology, 17, 1–13. DOI: 10.1371/journal.pcbi.1009275.
   Web of Science ®Google Scholar