SQUID: A Bayesian Approach for Physics-Informed Event Modeling

Sumantrak Mukherjee, Sebastian Josef Vollmer, Gerrit Großmann

Keywords: Events, PDE, Velocity Field, MCMC

TL;DR: Bayesian method to infer velocity field from event data

Abstract:

We study the spatiotemporal evolution of event processes (e.g., gunshots, vehicle thefts, earthquakes). Classical approaches model the intensity of a spatio-temporal point process directly. Instead, we propose to infer a latent velocity field that transports the event intensity via a continuity equation as a more interpretable and mechanistic alternative description.
The inference is performed in a Bayesian framework, using a Gaussian process to model the vector field. This provides calibrated uncertainty for both the vector field and the resulting forecasts. We evaluate the method on synthetic data to demonstrate efficient simulation and inference.

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Submission Number: 62