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Multivariate data having both continuous and discrete variables is known asmixed outcomes and has widely appeared in a variety of fields such as ecology,epidemiology, and climatology. In order to understand the probability structureof multivariate data, the estimation of the dependence structure among mixedoutcomes is very important. However, when location information is equipped withmultivariate data, the spatial correlation should be adequately taken intoaccount; otherwise, the estimation of the dependence structure would beseverely biased. To solve this issue, we propose a semiparametric Bayesianinference for the dependence structure among mixed outcomes while eliminatingspatial correlation. To this end, we consider a hierarchical spatial modelbased on the rank likelihood and a latent multivariate Gaussian process. Wedevelop an efficient algorithm for computing the posterior using the MarkovChain Monte Carlo. We also provide a scalable implementation of the model usingthe nearest-neighbor Gaussian process under large spatial datasets. We conducta simulation study to validate our proposed procedure and demonstrate that theprocedure successfully accounts for spatial correlation and correctly infersthe dependence structure among outcomes. Furthermore, the procedure is appliedto a real example collected during an international synoptic krill survey inthe Scotia Sea of the Antarctic Peninsula, which includes sighting data of finwhales (Balaenoptera physalus), and the relevant oceanographic data.

Semiparametric Copula Estimation for Spatially Correlated Multivariate  Mixed Outcomes: Analyzing Visual Sightings of Fin Whales from Line Transect  Survey