Statistics and Its Interface
Volume 12 (2019)
Semiparametric bayesian analysis of transformation spatial mixed models for large datasets
Pages: 549 – 560
In spatial mixed models (SMMs), it is commonly assumed that stationary spatial process and random errors independently follow the Gassian distribution. However, in some applications, this assumption may be inappropriate. To this end, this paper proposes a transformation spatial mixed models (TSMMs) to accommodate large dataset that follows the non-Gaussian distribution. With the help of Gibbs sampler algorithm, a semiparametric Bayesian approach is developed to make inference on TSMMs by using Bayesian P-splines to approximate transformation function, and a fixed number of known but not necessarily orthogonal spatial basis functions with multi-resolution analysis method to approximate nonstationary spatial process. Instead of Wishart distribution assumption for the prior of precision matrix of random effects, we consider Cholesky decomposition of the precision matrix, and specify the priors for unknown components in low unit triangular matrix and diagonal matrix. Simulation studies and an example are used to illustrate the proposed methodologies.
Gibbs sampler, large dataset, matrix decomposition, semiparametric Bayesian analysis, transformation spatial mixed models
2010 Mathematics Subject Classification
Primary 62F15. Secondary 62J05.
This research is supported by the National Natural Science Foundation of China (No. 11671349) and the Key Projects of the National Natural Science Foundation of China (No. 11731101), the National Social Science Fund of China (No. 17BTJ038), Yunnan Applied Basic Research Projects (No. 2016FD087).
Received 15 August 2018
Accepted 11 April 2019
Published 18 July 2019