A Markov model of land use dynamics

TL;DR

This paper discusses methods for estimating transition matrices in Markov chain models of land use, including MLE, Bayesian approaches, and testing model adequacy with sojourn times.

Contribution

It introduces new estimation techniques for Markov land use models and proposes a method to test model fit using sojourn times.

Findings

Bayes estimator approximated by MCMC improves transition matrix estimation.

Sojourn time method effectively tests model adequacy.

Comparison of MLE and Bayesian estimators demonstrates their respective advantages.

Abstract

The application of the Markov chain to modeling agricultural succession is well known. In most cases, the main problem is the inference of the model, i.e. the estimation of the transition matrix. In this work we present methods to estimate the transition matrix from historical observations. In addition to the estimator of maximum likelihood (MLE), we also consider the Bayes estimator associated with the Jeffreys prior. This Bayes estimator will be approximated by a Markov chain Monte Carlo (MCMC) method. We also propose a method based on the sojourn time to test the adequation of Markov chain model to the dataset.