Bayesian experimental design for models with intractable likelihoods.

Area of Science:

• Computational statistics
• Mathematical modeling
• Epidemiology
• Ecology

Background:

• Estimating parameters for complex models with intractable likelihoods is a significant challenge in statistical inference.
• Robust experimental design is crucial for efficient and accurate parameter estimation.
• Approximate Bayesian computation (ABC) offers a framework for inference without explicit likelihood functions.

Purpose of the Study:

• To develop and present a novel methodology for designing experiments to efficiently estimate parameters of models with computationally intractable likelihoods.
• To integrate robust experimental design principles with approximate Bayesian computation (ABC).
• To apply the methodology to stochastic models, specifically Markov process models of epidemics and macroparasite population evolution.

Main Methods:

• The methodology combines Markov chain Monte Carlo (MCMC) sampling for experimental design with approximate Bayesian computation (ABC) for parameter estimation.
• A utility function based on the precision of the ABC posterior distribution guides the experimental design.
• The ABC posterior is efficiently formed using the ABC rejection algorithm with pre-computed model simulations.

Main Results:

• The proposed methodology enables efficient parameter estimation without requiring computationally expensive likelihood evaluations.
• The approach was successfully applied to Markov process models, including epidemic models and macroparasite population evolution models.
• An assessment was made of information loss in a multivariate macroparasite model due to incomplete variable observation.

Conclusions:

• This work provides a robust and efficient framework for experimental design in the context of models with intractable likelihoods.
• The integration of MCMC and ABC offers a powerful tool for parameter estimation in complex stochastic systems.
• The methodology has practical implications for fields such as epidemiology and ecology where such models are prevalent.