Bayesian parameter inference and model selection by population annealing in systems biology

Area of Science:

• Systems Biology
• Computational Biology
• Statistical Modeling

Background:

• Parameter inference and model selection are crucial for mathematical modeling in systems biology.
• Approximate Bayesian computation (ABC) is commonly used but faces challenges with Monte Carlo methods for posterior distribution computation.
• Difficulty arises when posterior distributions are uniform or similar to priors, hindering representative parameter value identification.

Purpose of the Study:

• To introduce population annealing, a population Monte Carlo algorithm, for computing Bayesian posterior distributions within the ABC framework.
• To address parameter un-identifiability by proposing the use of a "posterior parameter ensemble."
• To enable Bayesian model selection in ABC by computing marginal likelihood and Bayes factors.

Main Methods:

• Application of population annealing to compute Bayesian posterior distributions in the ABC framework.
• Generation of a "posterior parameter ensemble" by sampling parameters from the posterior distribution.
• Computation of marginal likelihood within ABC using population annealing for Bayesian model selection.

Main Results:

• Population annealing proved efficient and convenient for generating posterior parameter ensembles.
• Simulations using the posterior parameter ensemble successfully reproduced existing data and predicted new data.
• Population annealing enabled the computation of marginal likelihood in ABC, facilitating model selection via Bayes factors.

Conclusions:

• Population annealing is an effective algorithm for parameter inference and model selection in systems biology using ABC.
• The "posterior parameter ensemble" approach enhances the reliability of model predictions and data reproduction.
• This work provides a robust computational framework for advancing Bayesian statistical methods in systems biology modeling.