Alive SMC(2) : Bayesian model selection for low-count time series models with intractable likelihoods.

Area of Science:

• Statistics
• Computational Biology
• Time Series Analysis

Background:

• Bayesian inference for time series models with intractable likelihoods presents significant computational challenges.
• Existing methods often rely on approximations or complex algorithms like reversible jump Markov chain Monte Carlo, limiting their applicability.

Purpose of the Study:

• To develop a novel, exact-approximate algorithm for Bayesian parameter inference and model choice in low-count time series models.
• To address the limitations of current methods by providing a more adaptive and less approximation-dependent approach.

Main Methods:

• Incorporation of an alive particle filter within a sequential Monte Carlo (SMC) framework.
• Development of a new algorithm termed alive SMC2, combining exact and approximate inference techniques.
• Application of the alive SMC2 algorithm to Markov process and integer autoregressive moving average models.

Main Results:

• The alive SMC2 algorithm demonstrates natural adaptivity and avoids the need for between-model proposals.
• The method successfully analyzes real-world biological datasets, including hospital-acquired pathogen incidence and prion disease cases.
• Performance is validated on various low-count time series models, showing robust inference capabilities.

Conclusions:

• The alive SMC2 algorithm offers a powerful and flexible tool for Bayesian analysis of challenging time series data.
• This novel approach enhances the accuracy and efficiency of inference for models with intractable likelihoods.
• The method's applicability to diverse biological datasets highlights its practical utility in computational biology and statistics.