Exploring Tolerance Selection and Multifidelity Techniques in an Approximate Bayesian Computation Framework - Sousa, Graziele Daiana Sena de (2024)
Statistical inference is essential in scientific research, providing the framework for drawing conclusions and making predictions based on data across various fields. The effectiveness of inference depends on how well mathematical models fit the data, with model fitting and parameter estimation being critical to ensuring model robustness and reliability. However, achieving accurate parameter estimation remains a significant challenge in statistical inference. The Bayesian framework has proven effective in addressing these challenges, offering a robust approach to making inferences. Bayesian inference often involves calculating the likelihood function, which can be computationally demanding or even infeasible in some cases. To address these, Approximate Bayesian Computation (ABC) has been developed, allowing for inference without explicit likelihood calculations. ABC methods approximate the posterior distribution using samples from the prior distribution, though they are computationally intensive due to the large number of model simulations required. A key issue in ABC is the selection of tolerance values, which significantly impacts the algorithm’s success. A variant of ABC methods is the Sequential Monte Carlo Approximate Bayesian Computation (ABC-SMC) method, which uses a sequence of decreasing tolerances to guide the algorithm through the parameter space, improving posterior approximation accuracy while reducing computational costs. This research focuses on analyzing tolerance selection techniques and applying multifidelity processes in ABC methodology, particularly in epidemiological problems. The study compares different tolerance strategies within ABC-SMC to improve inference accuracy and explores the integration of multifidelity techniques to reduce computational costs while maintaining or improving result accuracy. Two epidemiological models of varying complexity are used to test these methods. The study found that adaptive methods to select tolerances, particularly those based on percentiles, offered significant advantages in inference accuracy. Furthermore, the multifidelity technique effectively reduced computational costs without compromising accuracy, making it suitable for high-dimensional models.