Spatiotemporal Clustering with Neyman-Scott Processes via Connections to Bayesian Nonparametric Mixture Models

Area of Science:

• Computational Statistics
• Point Process Modeling
• Bayesian Inference

Background:

• Neyman-Scott processes (NSPs) are point process models adept at capturing clustered data in time or space.
• Their doubly stochastic formulation, involving latent events generating observed points, makes them suitable for phenomena like neural spike trains and document streams.
• Despite their utility, specialized inference algorithms for NSPs are less developed compared to similar Bayesian nonparametric mixture models.

Purpose of the Study:

• To establish novel connections between Neyman-Scott processes (NSPs) and Bayesian mixture models, specifically Dirichlet process mixture models (DPMMs) and mixture of finite mixture models (MFMMs).
• To adapt existing inference algorithms for DPMMs to facilitate scalable Bayesian inference for NSP models.
• To demonstrate the practical applicability of enhanced NSP inference methods on real-world spatiotemporal datasets.

Main Methods:

• Establishing theoretical links between Neyman-Scott processes (NSPs) and mixture of finite mixture models (MFMMs).
• Adapting the collapsed Gibbs sampling algorithm, commonly used for DPMMs, for efficient inference in NSPs.
• Applying the developed inference framework to analyze sequence detection in neural spike trains and event detection in document streams.

Main Results:

• A key connection was identified between NSPs and MFMMs, providing a bridge for inference.
• The adapted Gibbs sampling algorithm enables scalable Bayesian inference for NSP models.
• Successful application of the method demonstrated its potential for sequence and event detection in complex spatiotemporal data.

Conclusions:

• The established connections and adapted inference algorithms significantly advance the analytical capabilities for Neyman-Scott processes.
• Scalable Bayesian inference for NSPs opens new avenues for modeling complex clustered spatiotemporal data.
• The demonstrated applications highlight the practical value of NSPs in fields like neuroscience and text analysis.