The discrepancy measures in approximate Bayesian computation and applications in bioscience

Abstract

Background and Objective: Approximate Bayesian computation (ABC), identifying the parameters that yield simulated data resembling the observed data, is a powerful likelihood-free inference framework, and has been widely applied in bioscience including population model, epidemic model and so on. A major difficulty in ABC is how to accurately determine the level of the discrepancy for it has a crucial impact on the inference results of algorithms. In this paper, our aim is to propose a novel and valid discrepancy measure approach. Methods: By analyzing and comparing existing discrepancy measure methods, one finds they have obvious shortcomings including narrow adaptability and high computational cost. To overcome these deficiencies, an improved cosine similarity to assess the discrepancy in ABC is designed. First, both simulated data and observed data are converted into vectors, and then in virtue of the angle of them and the modulus of vectors, the similarity between the two data sets are measure. Results: The proposed discrepancy measure method achieves a comparable or higher posterior quality compared with the existing methods through four examples including Gaussian, Gaussian mixture, predator-prey and epidemic models. Conclusions: The statistical inference of complex biological models is a challenging task, and ABC algorithm can solve this problem well, but it needs to choose appropriate discrepancy measures. The results show that the improved cosine similarity is a extremely efficient discrepancy measurement method. Moreover, our work facilitates researchers to choose an appropriate discrepancy measure in practice.