arXiv subjects

Nicholas Grieshop

Publications and source records attributed to Nicholas Grieshop.

3 recordsLinked to original sources

arXiv2024

A Continuous-Time Stochastic Process for High-Resolution Network Data in Sports

Technological advances have paved the way for collecting high-resolution network data in basketball, football, and other team-based sports. Such data consist of interactions among players of competing teams indexed by space and time. High-resolution network data are vital to understanding and predicting the performance of teams, because the performance of a team is more than the sum of the strengths of its individual players: Whether a collection of players forms a strong team depends on the strength of the individual players as well as the interactions among the players. We introduce a continuous-time stochastic process as a model of interactions among players of competing teams indexed by space and time, discuss basic properties of the continuous-time stochastic process, and learn the stochastic process from high-resolution network data by pursuing a Bayesian approach. We present simulation results along with an application to Juventus Turin, Inter Milan, and other football clubs in the premier Italian soccer league.

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arXiv2023

Bayesian Ensemble Echo State Networks for Enhancing Binary Stochastic Cellular Automata

Binary spatio-temporal data are common in many application areas. Such data can be considered from many perspectives, including via deterministic or stochastic cellular automata, where local rules govern the transition probabilities that describe the evolution of the 0 and 1 states across space and time. One implementation of a stochastic cellular automata for such data is with a spatio-temporal generalized linear model (or mixed model), with the local rule covariates being included in the transformed mean response. However, in real world applications, we seldom have a complete understanding of the local rules and it is helpful to augment the transformed linear predictor with a latent spatio-temporal dynamic process. Here, we demonstrate for the first time that an echo state network (ESN) latent process can be used to enhance the local rule covariates. We implement this in a hierarchical Bayesian framework with regularized horseshoe priors on the ESN output weight matrices, which extends the ESN literature as well. Finally, we gain added expressiveness from the ESNs by considering an ensemble of ESN reservoirs, which we accommodate through model averaging. This is also new to the ESN literature. We demonstrate our methodology on a simulated process in which we assume we do not know all of the local CA rules, as well as a fire evolution data set, and data describing the spread of raccoon rabies in Connecticut, USA.

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arXiv2023

Data-Driven Modeling of Wildfire Spread with Stochastic Cellular Automata and Latent Spatio-Temporal Dynamics

We propose a Bayesian stochastic cellular automata modeling approach to model the spread of wildfires with uncertainty quantification. The model considers a dynamic neighborhood structure that allows neighbor states to inform transition probabilities in a multistate categorical model. Additional spatial information is captured by the use of a temporally evolving latent spatio-temporal dynamic process linked to the original spatial domain by spatial basis functions. The Bayesian construction allows for uncertainty quantification associated with each of the predicted fire states. The approach is applied to a heavily instrumented controlled burn.

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