Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes.

Area of Science:

• Statistics
• Epidemiology
• Computational Statistics

Background:

• Statistical modeling of temporal point patterns is crucial across various scientific fields.
• The Cox process is a widely used model for such data, featuring a stochastic intensity function.
• Existing models may lack efficiency or flexibility for complex temporal dynamics.

Purpose of the Study:

• To introduce a novel class of unidimensional Cox process models with state-switching parametric intensity functions.
• To develop an exact Bayesian inference methodology using Markov Chain Monte Carlo (MCMC) algorithms.
• To provide a computationally efficient and applicable method for analyzing large temporal point pattern datasets, including epidemic curves.

Main Methods:

• Development of a new Cox process model where the intensity function follows a continuous-time Markov chain.
• Implementation of exact Bayesian inference via MCMC algorithms, addressing reliability and specification issues.
• Validation through simulated data and real-world case studies, including epidemic data analysis.

Main Results:

• The proposed methodology enables computationally efficient Bayesian inference for complex Cox process models.
• The new class of models effectively captures dynamic changes in intensity functions.
• The approach demonstrates high efficiency and applicability in analyzing temporal point patterns, including epidemic forecasting.

Conclusions:

• The novel Cox process models and associated Bayesian inference methodology offer a powerful tool for statistical modeling of temporal point patterns.
• The method is particularly well-suited for analyzing epidemic curves, providing insights into disease dynamics.
• The computational efficiency allows for application to large datasets, advancing research in epidemiology and other fields.