A comparison of approximate versus exact techniques for Bayesian parameter inference in nonlinear ordinary...

Area of Science:

• Computational Science
• Mathematical Modeling
• Epidemiology

Background:

• Dynamical systems modeled by ordinary differential equations (ODEs) are crucial in science and engineering.
• Bayesian inference is a valuable tool for estimating unknown parameters in ODE models from experimental data.
• Exact Bayesian inference using Markov chain Monte Carlo (MCMC) can face challenges like slow convergence and poor mixing.

Purpose of the Study:

• To evaluate the efficacy of popular Approximate Bayesian Computation (ABC) methods in handling errors within ODE models.
• To investigate whether current ABC approaches accurately reflect epistemic uncertainties in parameter estimations.
• To compare the computational efficiency of ABC methods against exact Bayesian methods for ODE models.

Main Methods:

• Analysis of acceptance probability in ABC methods concerning discrepancy functions, tolerance, and error terms.
• Application of popular ABC methods, including MCMC ABC and SMC ABC, to ODE epidemiological models.
• Comparison with exact Bayesian inference techniques using both simulated and real-world malaria transmission data.

Main Results:

• Several popular ABC approaches inadequately model measurement errors in ODEs, impacting posterior distribution accuracy.
• The derived posterior distributions from these ABC methods do not precisely capture parameter uncertainties.
• ABC methods demonstrated minimal computational advantages over exact Bayesian methods when applied to the tested ODE models.

Conclusions:

• Existing ABC methods require refinement to properly account for observational errors in ODE models.
• Accurate quantification of epistemic uncertainty in parameter estimation is compromised by current ABC implementations for ODEs.
• The computational benefits of ABC over exact Bayesian inference for ODE models are often negligible in practice.