Computazione Bayesiana approssimata

Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quanti?es the support data lend to particular values of parameters and to choices among di?erent models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. Complex stochastic processes are often preferred over simple processes in modeling natural systems because they enable investigators to capture a greater proportion of the salient features of a system. However, probabilistic models resulting from such processes can lead to computationally intractable likelihood functions, posing challenges in the implementation of likelihood-based statistical inference methods. Since the most important object in Bayesian inference, the posterior distribution of the parameter given the data is, by Bayes Theorem, proportional to the likelihood, computationally intractable likelihoods translate to di?culties in Bayesian inference. Therefore, inference from models having computationally intractable likelihoods has received considerable attention in the Bayesian literature. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection.