Multiscale Multi‐Type Spatial Bayesian Analysis for High‐Dimensional Data With Application to Wildfires and Migration

ABSTRACT 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 a feedback mechanism that creates signal‐to‐noise dependence. We analyze point‐referenced remote sensing fire data from the National Aeronautics and Space Administration (NASA) and county‐level population change data provided by the U.S. Census Bureau's Population Estimates Program (PEP). We develop a multiscale multi‐type spatial Bayesian model that assumes the average number of fires is zero‐inflated normal, the incidence of fire is Bernoulli, and the percentage population change is normally distributed. This high‐dimensional dataset makes Markov chain Monte Carlo (MCMC) implementation infeasible. We bypass MCMC by extending a recently introduced computationally efficient Bayesian framework to directly sample from the exact posterior distribution, which includes a term to model signal‐to‐noise dependence. Such signal‐to‐noise dependence is known to be present in wildfire data, but is commonly not accounted for. A simulation study is used to highlight the computational performance of our method. In our analysis, we obtained predictions of wildfire probabilities, identified several useful covariates, and found that regions with many fires were associated with population change.