  Multivariate data having both continuous and discrete variables is known as
mixed outcomes and has widely appeared in a variety of fields such as ecology,
epidemiology, and climatology. In order to understand the probability structure
of multivariate data, the estimation of the dependence structure among mixed
outcomes is very important. However, when location information is equipped with
multivariate data, the spatial correlation should be adequately taken into
account; otherwise, the estimation of the dependence structure would be
severely biased. To solve this issue, we propose a semiparametric Bayesian
inference for the dependence structure among mixed outcomes while eliminating
spatial correlation. To this end, we consider a hierarchical spatial model
based on the rank likelihood and a latent multivariate Gaussian process. We
develop an efficient algorithm for computing the posterior using the Markov
Chain Monte Carlo. We also provide a scalable implementation of the model using
the nearest-neighbor Gaussian process under large spatial datasets. We conduct
a simulation study to validate our proposed procedure and demonstrate that the
procedure successfully accounts for spatial correlation and correctly infers
the dependence structure among outcomes. Furthermore, the procedure is applied
to a real example collected during an international synoptic krill survey in
the Scotia Sea of the Antarctic Peninsula, which includes sighting data of fin
whales (Balaenoptera physalus), and the relevant oceanographic data.
