Inference and Optimal Design for Nearest-Neighbour Interaction Models

TL;DR

This paper develops Bayesian inference methods and optimal experimental designs for spatial epidemic models on graphs, showing that sparsified lattices can provide more information than complete ones and analyzing estimator behavior for large clusters.

Contribution

It introduces MCMC algorithms for Bayesian inference in spatial epidemic models and demonstrates the benefits of sparsified lattice experiments for parameter estimation.

Findings

Sparsified lattice experiments can outperform complete lattice ones in information gain.

Developed effective MCMC algorithms for the model.

Proved probabilistic results on estimators for large infected clusters.

Abstract

We consider problems of Bayesian inference for a spatial epidemic on a graph, where the final state of the epidemic corresponds to bond percolation, and where only the set or number of finally infected sites is observed. We develop appropriate Markov chain Monte Carlo algorithms, demonstrating their effectiveness, and we study problems of optimal experimental design. In particular, we demonstrate that for lattice-based processes an experiment on a sparsified lattice can yield more information on model parameters than one conducted on a complete lattice. We also prove some probabilistic results about the behaviour of estimators associated with large infected clusters.