Advanced Bayesian methodologies for parametric and non-parametric inference of spatiotemporal phenomena

Real-world physical processes are rarely independent across space and time. For example, an above-average temperature in Urbana, IL, is often followed by a similar observation in nearby Champaign, IL, due to geographic proximity. Similarly, an increase in COVID-19 cases in one day may lead to higher cases the next day in the same city. These spatial and temporal correlations are critical for systems operating over large geographic areas and long time periods. Ignoring these correlations can result in significant underestimation of system vulnerabilities to external stressors. As a result, spatiotemporal models have become essential for capturing these dynamics, providing valuable tools for tasks like environmental monitoring, resource planning, and risk management. Spatiotemporal phenomena are observed across various domains, from natural hazards like earthquakes and floods to structural deterioration due to environmental factors. These phenomena exhibit considerable variability over different spatial and temporal scales. For example, a bridge may experience vehicle loads over short periods while also facing slow corrosion over decades. These multi-scale processes, coupled with a lack of comprehensive data and the computational expense of detailed physical models, make the modeling of spatiotemporal phenomena particularly challenging. One specific example of a complex spatiotemporal phenomenon is storm surge, which refers to the abnormal rise in seawater caused by hurricanes or other intense storms. Storm surge poses significant risks to coastal infrastructure and human populations, making it crucial to develop accurate models for prediction and real-time response. However, modeling storm surge involves integrating multiple interacting processes—such as oceanic dynamics, atmospheric conditions, and geographical factors—all operating on different spatial and temporal scales. Additionally, the sparsity of direct surge measurements further complicates this task. To address these challenges, this dissertation develops advanced statistical models and inference methods for spatiotemporal phenomena, with a particular focus on storm surge. The central approach involves the use of random fields and Bayesian inference, which offer flexible and probabilistic frameworks for handling uncertainty in both data and model predictions. Random fields provide smooth and adaptive representations of spatiotemporal processes, while Bayesian inference allows for the integration of sparse data with prior knowledge, producing comprehensive uncertainty estimates. Despite their advantages, traditional Bayesian methods such as Markov Chain Monte Carlo (MCMC) can be computationally prohibitive, particularly in large-scale spatiotemporal settings. This dissertation introduces several key advancements to address these computational challenges. For non- parametric random fields, the work adapts tools from Information Field Theory, specifically the Diagrammatic Perturbation Technique (DPT). DPT organizes the logarithm of the joint distribution into a Taylor series expansion, with each term represented by a diagram, simplifying complex Bayesian calculations. This approach is demonstrated with Gamma likelihoods and Gaussian priors, which are common in structural deterioration problems. The dissertation shows that DPT significantly reduces computational costs compared to MCMC, while maintaining accurate posterior estimates. For parametric models, the dissertation extends DPT to offer closed-form estimates of posterior moments, providing an efficient alternative to MCMC, especially in large datasets where the posterior deviates slightly from a Gaussian distribution. This method is applied to spatiotemporal models, linear regression, and generalized linear models, demonstrating its broad applicability. Finally, the dissertation presents a novel modeling approach for storm surge estimation within a Bayesian random field framework, leveraging DPT for efficient posterior estimation. This approach enables rapid, real-time predictions of storm surge, validated using historical NOAA data from the Gulf Coast. The model’s ability to capture uncertainty while delivering fast and accurate predictions offers a powerful tool for disaster preparedness and risk management in coastal regions.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Pandey, Aditya

Contributors dc:contributor

• Gardoni, Paolo
• Sriver, Ryan
• Meidani, Hadi
• Park, Trevor

• Spatiotemporal
• Gaussian Process
• Random Field
• Bayesian Inference
• Diagrammatic Perturbation Technique
• Deterioration
• Storm Surge

Statement dc:rights

• Copyright 2024 Aditya Pandey

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127485

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127485