This paper presents the results from employing survival analysis methods to model the probability distribution of the control time of forest fires. The Kaplan–Meier estimator, log–location–scale models, accelerated failure time models, and Cox proportional hazards (PH) models are described. Historical lightning and people-caused forest fire data from the Province of Ontario, Canada from 1989 through 2004 are employed to illustrate the use of the Cox PH model. We demonstrate how this methodology can be used to examine the association between the control time of a suppressed forest fire and local factors such as weather, vegetation and fuel moisture, as well as fire management variables including the response time between when a fire is reported and the initiation of suppression action. Significant covariates common to both the lightning and people-caused models were the size of the fire at the onset of initial attack, the Fine Fuel Moisture Code and the Initial Spread Index. The response time was also a significant predictor for the control time of lightning-caused fires, whereas the Drought Code and time of day of initial attack were significant for people-caused fires. Larger values of the covariates in these models were associated with larger survival probabilities.

In environmetrics, interest often centres around the development of models and methods for making inference on observed point patterns assumed to be generated by latent spatial or spatio‐temporal processes, which may have a hierarchical structure. In this research, motivated by the analysis of spatio‐temporal storm cell data, we generalize the Neyman–Scott parent–child process to account for hierarchical clustering. This is accomplished by allowing the parents to follow a log‐Gaussian Cox process thereby incorporating correlation and facilitating inference at all levels of the hierarchy. This approach is applied to monthly storm cell data from the Bismarck, North Dakota radar station from April through August 2003 and we compare these results to simpler cluster processes to demonstrate the advantages of accounting for both levels of correlation present in these hierarchically clustered point patterns. The Canadian Journal of Statistics 47: 46–64; 2019 © 2019 Statistical Society of Canada

In Canada, the Fire Weather Index (FWI) provides forest fire managers with an overall measure of fire danger. Specifically, the FWI is a numerical rating of the potential intensity of a forest fire based on its potential spread rate and the amount of vegetation available for combustion. In our analyses, we consider daily FWI time series, recorded over 42 fire seasons from a sample of fire-weather stations in Ontario, Canada. Graphical exploratory analyses of the data, including stalagmite plots (a new interactive, three-dimensional visualization tool), show that the FWI switches between epochs of nil and non-nil behaviour. This paper develops a framework for assessing sojourn times in these two phases. At some sites, the FWI process appears to begin each year as an approximate Markov process before gradually losing its Markovian character. However, a time-homogeneous discrete time Markov chain model is insufficient overall, because those sojourn times are not found to be geometrically distributed. Instead, the duration of epochs in each of these phases can be more accurately modelled using beta-geometric random variables which incorporate seasonality of phase-specific run length behaviour using local likelihood methods.