Direct Sampling of Bayesian Thin-Plate Splines for Spatial Smoothing

TL;DR

This paper introduces a direct sampling method for Bayesian thin-plate splines using radial basis functions, enabling efficient spatial smoothing without MCMC, and demonstrates the derivation of the prior and sampling scheme.

Contribution

It presents a novel direct sampling approach for Bayesian thin-plate spline models, reducing computational complexity compared to traditional MCMC methods.

Findings

Efficient direct sampling scheme for Bayesian thin-plate splines.

Avoids MCMC, reducing computational burden.

Demonstrates derivation of the prior and sampling method.

Abstract

Radial basis functions are a common mathematical tool used to construct a smooth interpolating function from a set of data points. A spatial prior based on thin-plate spline radial basis functions can be easily implemented resulting in a posterior that can be sampled directly using Monte Carlo integration, avoiding the computational burden and potential inefficiency of an Monte Carlo Markov Chain (MCMC) sampling scheme. The derivation of the prior and sampling scheme are demonstrated.