ABSTRACT
This chapter focuses primarily on the choice of the approximate Bayesian computation (ABC) tolerances that are used in the ABC kernel to penalise the dissimilarity between the simulated and observed summary statistics. It introduces lower and upper tolerances, and aims to specify non-symmetric values that offset any bias in the vanilla ABC sampler. The chapter makes the acceptance region wide enough to obtain a pre-specified degree of computational efficiency. It suggests that the quality of the ABC approximation can be sufficiently improved through the calibrations. The chapter describes the ABC accept/reject step as an equivalence test rather than the standard point null hypothesis tests. It expands on the advantages of interpreting the ABC accept/reject step as the outcome of an equivalence test. The chapter focuses on the case where the data and simulations are just real values from a normal distribution. It discusses how one-sample equivalence hypothesis tests can be used within ABC.
