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Which is the best description of approximate Bayesian computation?
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.
Why are computational methods used in Bayesian inference?
Another prescient point was made by Rubin when he argued that in Bayesian inference, applied statisticians should not settle for analytically tractable models only, but instead consider computational methods that allow them to estimate the posterior distribution of interest. This way, a wider range of models can be considered.
What makes a non negligible approximation of the posterior?
Approximation of the posterior. A non-negligible comes with the price that one samples from instead of the true posterior . With a sufficiently small tolerance, and a sensible distance measure, the resulting distribution should often approximate the actual target distribution reasonably well.
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 simulations used to approximate the likelihood function?
All ABC-based methods approximate the likelihood function by simulations, the outcomes of which are compared with the observed data. More specifically, with the ABC rejection algorithm—the most basic form of ABC—a set of parameter points is first sampled from the prior distribution.
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.