Deterministic Objective Bayesian Analysis for Spatial Models

TL;DR

This paper develops deterministic algorithms for objective Bayesian analysis of spatial Gaussian process models, improving prediction and inference using advanced optimization and sparse grid techniques.

Contribution

It introduces novel deterministic algorithms for Bayesian spatial modeling based on noninformative priors, utilizing trust-region optimization and adaptive sparse grids.

Findings

Algorithms enable efficient Bayesian prediction and inference.

Implementation available at GitHub for reproducibility.

Enhances objective Bayesian analysis for spatial data.

Abstract

Berger et al. (2001) and Ren et al. (2012) derived noninformative priors for Gaussian process models of spatially correlated data using the reference prior approach (Berger, Bernardo, 1991). The priors have good statistical properties and provide a basis for objective Bayesian analysis (Berger, 2006). Using a trust-region algorithm for optimization with exact equations for posterior derivatives and an adaptive sparse grid at Chebyshev nodes, this paper develops deterministic algorithms for fully Bayesian prediction and inference with the priors. Implementations of the algorithms are available at https://github.com/rnburn/bbai.