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A set of probabilities along with corresponding quantiles are often used to define predictive distributions or probabilistic forecasts. These quantile predictions offer easily interpreted uncertainty of an event, and quantiles are generally…

This paper considers the problem of forecasting mortality rates. A large number of models have already been proposed for this task, but they generally have the disadvantage of either estimating the model in a two-step process, possibly…

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be…

We discuss ways to measure duration in a power transmission system resilience event by modeling outage and restore processes from utility data. We introduce novel Poisson process models that describe how resilience events progress and…

Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…

Given the increasing prevalence of wildland fires in the Western US, there is a critical need to develop tools to understand and accurately predict burn severity. We develop a machine learning model to predict post-fire burn severity using…

Climate change has intensified the frequency and severity of wildfires, making rapid and accurate prediction of fire spread essential for effective mitigation and response. Physics-based simulators such as FARSITE offer high-fidelity…

We introduce a simple and wide class of multifractal spatial point patterns as Cox processes which intensity is multifractal, i.e., the class of Poisson processes with a stochastic intensity corresponding to a random multifractal measure.…

The increasing incidence and severity of wildfires underscores the necessity of accurately predicting their behavior. While high-fidelity models derived from first principles offer physical accuracy, they are too computationally expensive…

In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…

Expansion planning problems refer to the monetary and unit investment needed for energy production or storage. An inherent element in these problems is the element of stochasticity in various aspects, such as the generation output of the…

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

In this paper, we introduce a risk process, namely, the mixed fractional risk process (MFRP) in which the number of claims in the associated claim process are modelled using the mixed fractional Poisson process (MFPP). The covariance…

Wildfires have significantly increased in the United States (U.S.), making certain areas harder to live in. This motivates us to jointly analyze active fires and population changes in the U.S. from July 2020 to June 2021. The available data…

This article introduces estimators of trend and seasonality for time series of point processes. We assume the point processes follow a temporal or spatial doubly-stochastic Poisson model with log-Gaussian intensity functions. The proposed…

Accurate prediction of wildfire spread is crucial for effective risk management, emergency response, and strategic resource allocation. In this study, we present a deep learning (DL)-based framework for forecasting the final extent of…

Wildfire forecasting has been one of the most critical tasks that humanities want to thrive. It plays a vital role in protecting human life. Wildfire prediction, on the other hand, is difficult because of its stochastic and chaotic…

The USDA Forest Inventory and Analysis (FIA) program conducts a national forest inventory for the United States through a network of permanent field plots. FIA produces estimates of area averages and totals for plot-measured forest…

Predicting future states in uncertain environments, such as wildfire spread, medical diagnosis, or autonomous driving, requires models that can consider multiple plausible outcomes. While diffusion models can effectively learn such…

Forecasting costs is now a front burner in empirical economics. We propose an unconventional tool for stochastic prediction of future expenses based on the individual (micro) developments of recorded events. Consider a firm, enterprise,…