Spatiotemporal Models and Inference

Team

Dr. Jonas Wahl (lecturer)
Felix Jahn, Pascal Schumann (assistants)

Content

In many scientific fields, data is not just tied to a single location or a single moment in time: it evolves over both space and time. Whether tracking the spread of infectious diseases, predicting climate patterns, modeling traffic flows, or analyzing environmental pollution, understanding how variables change across both dimensions is crucial. This is where spatiotemporal modeling comes in.

Spatiotemporal models aim to capture dependencies and relationships in data that vary over time and across geographical locations. Unlike purely spatial or purely temporal models, these approaches integrate both dimensions, allowing us to uncover trends, make predictions, and quantify uncertainties in dynamic systems. Spatiotemporal models can be of different types:

• Deterministic models, based on physical laws or equations (e.g., fluid dynamics for weather modeling).
• Statistical models, which use probability distributions to describe uncertainties (e.g., Gaussian processes, Bayesian hierarchical models).
• Machine learning models, which learn patterns from large datasets using neural networks, random forests, or deep learning approaches.

The latter two were the main focus of this seminar. Applications of spatiotemporal modeling are found across the sciences, from forecasting the spread of diseases and analyzing temperature changes over decades to optimizing transportation networks and tracking animal migration or deforestation. The seminar covered the theoretical underpinnings of spatiotemporal statistics, Bayesian approaches and hierarchical models, and machine learning techniques for complex spatiotemporal data.

Format

A block seminar for up to 10 participants, with a kick-off in June. Each participant gave a 60-minute presentation. Grading: presentation (50%), participation in the talks of fellow participants and the discussion (25%), and a final report on the topic (25%).

Prerequisites: successful participation in a machine or deep learning course, or a background in statistical modeling, for instance from a course on statistics or stochastic processes.

Topics

1. Statistics for Spatiotemporal Data, Chapter 2: Statistical preliminaries
2. Statistics for Spatiotemporal Data, Chapter 3: Fundamentals of Temporal Processes
3. Statistics for Spatiotemporal Data, Chapter 4: Fundamentals of Spatial Random Processes
4. Introduction to Gaussian processes (lecture notes here and here, and the book)
5. Coding tutorial on spatial Gaussian processes (based on this blog post and this one)
6. Introduction to point processes (lecture notes here, slides here and here)
7. Coding tutorial on point processes (with the tick package, this simulator, these Jupyter notebooks, or spatial point patterns in R)
8. Scalable spatiotemporal prediction with Bayesian neural fields, with a coding tutorial on Bayesian neural fields
9. A Bayesian machine-learning approach for spatiotemporal prediction of COVID-19 cases
10. Spatial-temporal graph neural networks for groundwater data

Organization

All information and materials are available in the CMS.