Evaluation of Tolerance Selection Strategies and Multifidelity Techniques in ABC Methods

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Approximate Bayesian Computation (ABC) methods provides a flexible and robust framework for solve model fitting problems, particularly pertinent to complex models with intractable likelihood functions. This methodology is based on approximating a simulated parameter values through auxiliary data and evaluating the distance of this data with the true dataset. Effective implementation of these methods require reasonable decisions to be made about the selection of ABC techniques and how to implement the algorithm to ensure computational efficiency. A comprehensive understanding of these factors facilitates a more accurate inference about the model. This study aims to explore the impact of the tolerance selection and the integration of Multifidelity techniques to the convergence and cost of the method. In the initial approach, three methods of choosing tolerances are employed: a predefined vector, a percentile calculation, and a percentage calculation based on the distance vector obtained from model simulations, in order to verify the most effective strategy for the improvement of the inference process. Subsequently, the optimal approach of tolerances selection is combined with Multifidelity techniques to reduce the computational cost. This methodology is applied in the examination of infectious disease models of differential equations. This study aims to highlight the importance of careful decision-making when using ABC methods, through the evaluation of some approaches for choosing tolerance in combination with techniques that aim to reduce the computational cost in constructing samples in ABC methods. Through this analysis, we focus our efforts on trying to demonstrate insights about gains in computational efficiency and accuracy in results.