How is approximate Bayesian computation used in statistical inference?
Approximate Bayesian computation ( ABC) constitutes a class of computational methods rooted in Bayesian statistics that can be used to estimate the posterior distributions of model parameters. In all model-based statistical inference, the likelihood function is of central importance,…
How is the Bayes theorem related to conditional probability?
A common incarnation of the Bayes theorem relates the conditional probability (or density) of a particular parameter value given data to the probability of given by the rule: where denotes the posterior, the likelihood, the prior, and the evidence (also referred to as the marginal likelihood or the prior predictive probability of the data).
How is a sample from the posterior of model parameters obtained?
A sample from the posterior of model parameters was obtained by accepting/rejecting proposals based on comparing the number of segregating sites in the synthetic and real data. This work was followed by an applied study on modeling the variation in human Y chromosome by Jonathan K. Pritchard et al. using the ABC method.
How are ABC methods used in statistical inference?
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.
Which is the outcome of the ABC rejection algorithm?
The outcome of the ABC rejection algorithm is a sample of parameter values approximately distributed according to the desired posterior distribution, and, crucially, obtained without the need to explicitly evaluate the likelihood function. Parameter estimation by approximate Bayesian computation: a conceptual overview.
Why is the likelihood function important in statistical inference?
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 quantifies the support data lend to particular values of parameters and to choices among different models.