A Conditional Autoregressive Gaussian Process for Irregularly Spaced Multivariate Data with Application to Modelling Large Sets of Binary Data

摘要: A Gaussian conditional autoregressive (CAR) formulation is presented that permits the modelling of spatial dependence and between multivariate random variables at irregularly spaced sites so capturing some advantages geostatistical approach. The model benefits not only from explicit availability full conditionals but also computational simplicity precision matrix determinant calculation using a closed form expression involving eigenvalues submatrix. introduction covariates into adds little complexity to analysis thus method can be straightforwardly extended regression models. model, because its simplicity, well suited application fully Bayesian large data sets measurements with ordering. An extension spatio-temporal considered. Here, we demonstrate use in bivariate binary where observed modelled as sign hidden CAR process. case study over 450 presence or absence each two species rain forest trees site presenteds Markov chain Monte Carlo (MCMC) methods are implemented obtain posterior distributions all unknowns. MCMC works simulated tree biodiversity set.