Importance Sampling for Cost-Optimized Estimation of Burn Probability Maps in Wildfire Monte Carlo Simulations

Background: Wildfire modelers rely on Monte Carlo simulations of wildland fire to produce burn probability maps. These simulations are computationally expensive. Methods: We study the application of importance sampling to accelerate the estimation of burn probability maps, using L2 distance as the metric of deviation. Results: Assuming a large area of interest, we prove that the optimal proposal distribution reweights the probability of ignitions by the square root of the expected burned area divided by the expected computational cost and then generalize these results to the assets-weighted L2 distance. We also propose a practical approach to searching for a good proposal distribution. Conclusions: These findings contribute quantitative methods for optimizing the precision/computation ratio of wildfire Monte Carlo simulations without biasing the results, offer a principled conceptual framework for justifying and reasoning about other computational shortcuts, and can be readily generalized to a broader spectrum of simulation-based risk modeling.