Determining changes in historical forest fire frequency from a time-since-fire map

Date

2010-01-08T22:06:43Z

Authors

Reed, William J.

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Abstract

The paper deals with 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.

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Keywords

fire frequency, fire history, time-since-fire map, quasi likelihood, change points, selection bias, Brownian bridge, Poisson clumping heuristic, model selection, backwards elimination

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