Deterministic Objective Bayesian Analysis for Spatial Models

2023/07/18 by Ryan Burn, Burn, Ryan
Chemistry · Computer Science · Environmental Science · #60G15 #Atmospheric and Environmental Gas Dynamics #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Spectroscopy and Chemometric Analyses

paper · pdf · doi:10.48550/arxiv.2307.08997

openalex publication_date 2023/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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