Determining Changes in Historical Forest Fire Frequency From a Time-Since-Fire Map

This article describes methods of identifying change points for historical forest fire frequency (hazard rate) using data from a time-since-fire map and an overdispersed survival model with associated quasi-likelihood function. A method of obtaining an approximate P value for testing the null hypothesis of no change points (homogeneous hazard), against the alternative of one change point, using the likelihood ratio statistic, is presented. It is based on use of the Poisson clumping heuristic for the maximum of a self-normalized Brownian bridge process. Iterative methods of determining multiple change points (analogous to methods of variable selection in regression) are discussed. Once change points have been identified, confidence intervals for the fire frequency in the intervening epochs can be obtained using likelihood ratio methods. Various procedures are applied to time-since-fire map data for Glacier National Park and backwards elimination found to give the most plausible results. Three of the four change points identified correlate well with established historical processes or events.

Key Words
Backwards elimination; Brownian bridge; Change points; Forest fire history; Model selection; Poisson clumping heuristic; Quasi-likelihood; Selection bias.

William J. Reed is Professor, Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria B.C., Canada V8W 3P4 (E-mail: reed@math.uvic.ca).