A spatio-temporal analysis was performed on wildland fire intensity measurements (thermal temperature data) from a prescribed burn at an ecological research center in Georgia, to better understand the variables and environmental conditions that promote fire spread in a longleaf pine ecosystem (Pinus palustris Mill.). This ecosystem is prevalent in the Southeastern U.S. and prescribed burning is a vital tool for maintaining the ecological function and biodiversity unique to this forest. Measuring fire behavior (spread and intensity) is critical for advancing fire behavior modeling, understanding fire effects and supporting initiatives to support public safety. The infrared cameras used to measure fire intensity had limitations allowing them to only record temperatures strictly above 300 ^∘ C, where plant material combustion mainly occurs. This censoring of temperature values below 300 ^∘ C posed a challenge that initiated this study, which was overcome by augmenting the data set by extrapolating temperatures down to the day’s ambient temperature. This extrapolation is a major focus of this analysis. Spatio-temporal models were applied to these data, and several aspects of the models were evaluated, such as the chosen hyperparameters, the spatial covariance structure, and the prior distributions for the parameters. A sensitivity analysis tested the robustness of the model to several heuristic choices of tuning parameters allowing for multiple reconstructions of the censored data. The model fit to the reconstructed data sets containing extrapolated temperatures appeared to give relevant insight into fire behavior phenomenon. The effects of the covariates in the model, such as wind speed, wind direction, their interaction, and several vegetative fuel variables, such as coarse and fine fuels were significant. These statistical models provide more complete datasets of fire intensity that can be used to evaluate physics-based fire-atmosphere models of fire behavior.
Discriminating among competing statistical models for experimental data is of interest for physical science. While right-skewed experimental measurements commonly approximate a lognormal distribution, among many others, substantial deviations occur at the extremes of the distribution, suggesting that alternative models may provide better fits in certain contexts. In many practical contexts, the choice of a single underlying distribution has significant implications, such as estimating the proportion of dwellings exceeding regulatory reference radon levels. We employ a Bayesian approach to model selection, utilizing Bayes factors and posterior model probabilities to compare suitable distributions applied to radon concentration data from Gran Canaria. Using non-informative priors appropriate for shape-scale family distributions, we calculate marginal densities and derive evidence metrics that transcend the limitations of conventional frequentist goodness-of-fit tests. We found strong evidence against the Gamma model and mild/weak evidence for the LogLogistic over the LogNormal distribution. We also offer a Bayesian model averaging strategy that weights the LogLogistic and LogNormal distributions by their posterior probability to create BMA mixture that improves dwelling exceedance frequency estimates across regulatory reference levels.
This paper explores variance or mean squared error estimation in the design-based inferential framework, focusing on a broad class of estimators and sampling schemes commonly employed in spatial surveys for both continuous populations and finite populations of areas. Specifically, the use of the pseudo-population bootstrap is proposed. It involves constructing a spatial pseudo-population from the sample data using the inverse distance weighting interpolator and then selecting bootstrap samples from the pseudo-population using the same sampling scheme adopted to select the original sample. The properties of the resulting variance or mean squared error estimators are theoretically investigated and empirically assessed through a simulation study. Two case studies are considered.
Caribbean islands are increasingly affected by rainfall variability, with alternating droughts and extreme precipitation events threatening water security and increasing flood risk. This study investigates the spatio-temporal variability of rainfall in the Guadeloupe archipelago using daily observations from 20 meteorological stations over the period of 2005–2014. A dynamic clustering approach highlights five areas of consistent rainfall linked to topography and exposure to trade winds, with average rainfall ranging from 3.3 to 9.8 mm day ^-1 . In addition, an algorithm specifically designed to preserve extreme rainfall values was constructed for generating data within the resulting clusters. To capture both regular fluctuations and extreme events, we develop an Adapted Black–Scholes Model with Jumps and Regimes (ABSMJR), formulated as a stochastic differential equation comprising a drift term, a diffusion term driven by Brownian motion, jump components accounting for extreme events, and a regime-switching mechanism governing structural changes in the dynamics. Model parameters are estimated by maximum likelihood method. Model performance is assessed using MASE, RMSE, Theil’s U statistic, and extreme-event metrics. Compared with SARIMA, SARIMA-GARCH, and GLM Gamma, the ABSMJR framework provides a more accurate representation of extreme rainfall events (F1 score = 0.608) while maintaining satisfactory predictive performance. The proposed approach offers a useful tool for reservoir management, agricultural planning, and flood-risk assessment and can be transferred to other tropical regions exhibiting similar rainfall variability.
The proportional hazards (PH) model is one of the most widely used models in survival analysis, typically assuming a log-linear relationship between covariates and the hazard function. However, in the context of spatial survival data, where the time-to-event variable is associated with a spatial location within a given domain, this assumption is often unrealistic in capturing spatial effects. Thus, this paper proposes modeling the location effect through a nonparametric function of spatial location. The function is approximated using finite element methods on a triangulated mesh to accommodate irregular domains. Estimation is carried out within the classical partial likelihood framework, with smoothness of the spatial effect enforced through differential penalization. Using sieve methods, we establish the consistency and asymptotic normality of the parametric component. Simulations and two empirical applications demonstrate superior performance compared to existing approaches.
