Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation

Area of Science:

• Computational epidemiology
• Statistical inference
• Stochastic processes

Background:

• Compartmental models are crucial for understanding epidemic dynamics.
• Incorporating intrinsic stochasticity is essential for accurate epidemic modeling.
• Existing Bayesian inference methods may face scalability and flexibility challenges.

Purpose of the Study:

• To introduce a novel Bayesian inference method for compartmental models that accounts for process stochasticity.
• To develop a Data Augmented MCMC approach using Poisson Random Measure (PRM) augmentation.
• To enhance the flexibility and scalability of epidemic model inference.

Main Methods:

• Formulating a SIR-type Markov jump process as a stochastic differential equation with respect to a PRM.
• Simulating process trajectories deterministically from parameter values and PRM realizations.
• Augmenting parameter space with unobserved PRM values for Metropolis-Hastings sampling.

Main Results:

• The PRM-augmented MCMC method demonstrates efficient simulation-based inference adaptable across models.
• This approach scales better with epidemic size and offers greater flexibility than Gibbs sampling-based methods.
• PRM augmentation provides posterior estimates of stochasticity, enabling model validation and identification of underfitting.

Conclusions:

• PRM-augmented MCMC offers a coherent framework for stochastic epidemic model inference.
• Explicitly inferring process stochasticity aids in robust model validation.
• The method successfully identified limitations in a simple SEIR model applied to Zika epidemic data.