Bayesian Analysis of Spatial Generalized Linear Mixed Models with Laplace Random Fields

2019/07/25 by Adam Walder, Walder, Adam, Ephraim M. Hanks +1
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.1907.11077

openalex publication_date 2019/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gaussian random field (GRF) models are widely used in spatial statistics to capture spatially correlated error. We investigate the results of replacing Gaussian processes with Laplace moving averages (LMAs) in spatial generalized linear mixed models (SGLMMs). We demonstrate that LMAs offer improved predictive power when the data exhibits localized spikes in the response. SGLMMs with LMAs are shown to maintain analogous parameter inference and similar computing to Gaussian SGLMMs. We propose a novel discrete space LMA model for irregular lattices and construct conjugate samplers for LMAs with georeferenced and areal support. We provide a Bayesian analysis of SGLMMs with LMAs and GRFs over multiple data support and response types.

Citations

• Examples of Adaptive MCMC
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• Bayesian Analysis of Binary and Polychotomous Response Data

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