B1643
Title: Bayesian semiparametric spatial model using template model builder (TMB)
Authors: Joaquin Cavieres - Gottingen University (Germany) [presenting]
Abstract: Bayesian computation can become prohibitive when dealing with a large number of spatial observations. For instance, using a Gaussian random field (GRF) as a spatial random effect incurs significant computational costs for estimation due to the need for factorizing a dense $nxn$ covariance matrix. The utilization of a low-rank approximation of a thin plate spline as a spatial random effect within a Bayesian semiparametric spatial model (BSSM) is proposed. Since the kernel matrix is dense, the method introduced by the prior study is employed, which utilizes the Lanczos iteration to obtain a truncated eigen-decomposition in $O(kn^2)$ operations. This is achieved iteratively by constructing a tri-diagonal matrix, with eigenvalues converging as iterations progress. For Bayesian inference, the Hamiltonian Monte Carlo algorithm is employed, provided by the probabilistic software Stan. A simulation study shows that the BSSM model provides faster estimation compared to an approximated GRF model. In a real application, the BSSM model outperforms the approximated GRF model based on the leave-one-out cross-validation (LOOCV) criterion and incurs significantly lower computational costs. Its primary advantage stems from its straightforward parameterization and swift chain convergence, even when dealing with complex models.
