Statistical methods for estimating historical fire frequency from multiple fire-scar data

This paper considers the statistical analysis of fire-interval charts based on fire-scar data. Estimation of the fire interval (expected time between scar-registering fires at any location) by maximum likelihood is presented. Because fires spread, causing a lack of independence in scar registration at distinct sites, an overdispersed binomial model is used, leading to a two-variable quasi-likelihood function. From this, point estimates, standard errors, and approximate confidence intervals for fire interval and related quantities can be derived. Methods of testing for the significance of spatial and temporal differences are also discussed. A simple example using artificial data is given to illustrate the computational steps involved, and an analysis of real fire-scar data is presented.