A latent model to detect multiple clusters of varying sizes

Area of Science:

• Statistics
• Data Science
• Computational Statistics

Background:

• Temporal event data often exhibits clustering.
• Detecting these clusters is crucial for understanding underlying processes.
• Existing methods like the scan statistic have limitations in detecting multiple or varying-sized clusters.

Purpose of the Study:

• To develop a novel latent model for detecting temporal clustering of events.
• To create a likelihood-based inference framework for parameter estimation and cluster identification.
• To offer a method capable of simultaneously detecting multiple clusters of diverse sizes.

Main Methods:

• Development of a latent statistical model mimicking data-generating processes.
• Application of model selection for determining the optimal number of clusters.
• Implementation of likelihood inference and a Monte Carlo Expectation-Maximization algorithm for parameter estimation and cluster detection.
• Comparison with the classical scan statistic and least squares-based procedures.

Main Results:

• The proposed methodology effectively estimates model parameters and identifies temporal clusters.
• Model selection techniques successfully determine the number of clusters.
• The method demonstrates efficiency in detecting multiple clusters of varying sizes.
• Simulation studies and real data applications confirm the methodology's effectiveness and efficiency compared to competing methods.

Conclusions:

• The developed latent model and likelihood-based inference provide a robust framework for temporal cluster detection.
• This approach offers advantages over traditional methods, particularly in scenarios with multiple, heterogeneous clusters.
• The methodology is validated through empirical applications and simulations, highlighting its practical utility and statistical efficiency.