Predicting rare events using training data from stratified sampling designs, with application to human-caused wildfire prediction

Response-based sampling is often used in modelling rare events from large, imbalanced data for efficiency. When modelling the event with logistic regression, the sampling design may be adjusted for using sampling weights or an offset. We propose a stratified sampling design for modelling rare events with large data which improves on previous methods by providing unbiased estimates of the standard errors of the coefficients in a multiple logistic regression scenario. We use multiple intercepts to model the incidence in the sampled data, then adjust each intercept via a stratum-specific offset. Our simulations provide no evidence of bias in the estimated logistic regression coefficients or their standard errors. We apply this method to spatio-temporal, fine-scale human-caused fire occurrence modelling for a region in northwestern Ontario, Canada, illustrating how the stratified sampling approach results in more locally precise estimates of fire occurrence.