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

## TL;DR

This paper explores replacing Gaussian random fields with Laplace moving averages in spatial generalized linear mixed models, showing improved prediction for data with localized spikes while maintaining similar inference and computational efficiency.

## Contribution

It introduces a novel discrete space LMA model for irregular lattices and develops conjugate samplers, expanding Bayesian spatial modeling capabilities.

## Key findings

- LMAs improve predictive accuracy for spike-like spatial data
- Parameter inference remains consistent with Gaussian models
- Computational methods are comparable to existing Gaussian SGLMMs

## 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.