Estimation of Temporal Variations in Historical Fire Frequency from Time-Since-Fire Map Data
This paper describes an improved statistical methodology for estimating historical forest fire frequencies from time-since-fire map data. Of particular interest is the question of estimating fire frequency in temporally distinct epochs. Unlike previous graphical and ad hoc methods, the new methodology is firmly grounded within the established statistical paradigm of likelihood inference. In addition, in contrast to earlier methods, it takes into account the fact that surviving stands which originated in earlier epochs, have been subject to different hazards of burning as they have lived through more recent epochs. Neglecting this fact leads to overestimates of the fire frequency in the more recent epochs. Procedures for obtaining maximum likelihood estimates and likelihood ratio confidence intervals for the fire frequency in each epoch are developed, along with a likelihood ratio test to assess whether the fire frequencies in distinct epochs were significantly different. This test is not strictly valid when the change points separating epochs are suggested from exploratory data analysis; rather it is developed assuming that change points are determined independently of the data. This distinction, which is necessary to avoid selection bias, has not been noted before. The fact that forest fire is a contagious process, with consequent spatial autocorrelation in time-since-fire observations, is taken into account through the use of an overdispersed model, with associated quasi-likelihood function. This aspect has been ignored, by and large, in previous analyses which have implicitly assumed independence of observations. An example is given in which the method is applied to published fire history data from the Kananaskis Valley. The results indicate that the previous analysis overestimated the fire frequency for the most recent epoch. The conclusions of other studies concerning temporal changes in fire frequency may need to be reconsidered. For. Sci. 44(3):465-475.
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