Multiscale Multi-Type Spatial Bayesian Analysis of Wildfires and Population Change That Avoids MCMC and Approximating the Posterior Distribution

In recent years, wildfires have significantly increased in the United States (U.S.), making certain areas harder to live in. This motivates us to jointly analyze active fires and population changes in the U.S. from July 2020 to June 2021. The available data are recorded on different scales (or spatial resolutions) and by different types of distributions (referred to as multi-type data). Moreover, wildfires are known to have feedback mechanism that creates signal-to-noise dependence. We analyze point-referenced remote sensing fire data from National Aeronautics and Space Administration (NASA) and county-level population change data provided by U.S. Census Bureau's Population Estimates Program (PEP). To do this, we develop a multiscale multi-type spatial Bayesian hierarchical model that assumes the average number of fires is zero-inflated normal, the incidence of fire as Bernoulli, and the percentage population change as normally distributed. This high-dimensional dataset makes Markov chain Monte Carlo (MCMC) implementation infeasible. We bypass MCMC by extending a computationally efficient Bayesian framework to directly sample from the exact posterior distribution, referred to as Exact Posterior Regression (EPR), which includes a term to model feedback. A simulation study is included to compare our new EPR method to the traditional Bayesian model fitted via MCMC. In our analysis, we obtained predictions of wildfire probabilities, identified several useful covariates, and found that regions with many fires were directly related to population change.