Date of Award

Summer 2025

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

David Hitchcock

Abstract

An analysis of fire data sets resulting from controlled burns was performed. Spatio-temporal models were applied to the data sets to determine which covariates are significant in predicting fire temperature. The data sets were censored and only contain temperatures above 300C, due to a limitation in the measuring device. To handle the censoring, an extrapolation was used to reconstruct the temperatures below 300C. Models were created and run for a data set with the extrapolated temperatures and a data set with all censored temperatures removed. Several aspects of the model were evaluated, such as the chosen hyperparameters, the spatial covariance structure, and the prior distributions for the parameters. Once the models were properly tuned, a comparison of the results was conducted. The models' predictive abilities were then tested. To evaluate out-of-sample predictive power, the models predicted temperatures on simulated grids of the covariates. Predictions were also calculated on sections of the true grid whose temperature values were held out, to test their predictions against observed temperatures. This allowed for numerical measurements of accuracy like the sum of squared errors. Lastly, an ensemble prediction was used which required creating several models that vary in some way, such as parameters or hyperparameters. Then a weighted average of the varying model predictions produced one superior prediction. The final weights chosen were based on functional data depth and the roughness of the prediction curves. Both visual and numerical results are presented. A separate analysis was conducted to compare the shape and magnitude of empirical and computer simulated power release curves for fire data sets. The computer-based simulation called QUIC-Fire is meant to help with several real-world applications, giving ecological researchers working with controlled burns a means to compare, evaluate, and design burn plans. To compare the shapes of the empirical and simulated curves, specific statistics were gathered for both data sets and compared visually and with a permutation test. Additionally, the entire curves were compared using a permutation test with a test statistic related to the idea of functional data depth. Both numerical and visual results from the comparison of how similar QUIC-Fire is to empirical fire data are presented. Any discrepancies and potential causes are also presented.

Rights

© 2025, Jedidiah Olof Lindborg

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