1,721,016 research outputs found
Approximate Bayesian computation and applications
No full textRecent developments allow Bayesian analysis also when the likelihood function
is intractable, that means it is analytically unavailable or computationally prohibitive to evaluate. These methods are known as “approximate Bayesian computation” (ABC) or likelihood-free methods and are characterized by the fact that the approximation of the posterior distribution is obtained without explicitly evaluating the likelihood function. This kind of analysis is popular in genetic and financial settings. In this work, ABC and some possible applications will be presented
Delayed acceptance with prefetching
No full textMCMC algorithms such as Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions as exemplified by
huge datasets. We offer an approach to reduce the computational costs of such algorithms by a simple and universal divide-and-conquer strategy.
The idea behind the generic acceleration is to divide the acceptance step into several parts, aiming at a major reduction in computing time that
outranks the corresponding reduction in acceptance probability. The division decomposes the “prior x likelihood” term into a product such that
some of its components are much cheaper to compute than others. Each of the components can be sequentially compared with a uniform variate, the
first rejection signalling that the proposed value is considered no further. The approach can in turn be accelerated as part of a prefetching algorithm
taking advantage of the parallel abilities of the computer at hand. We illustrate those accelerating features on a series of toy and realistic examples
Approxiamte Bayesian Methods for copula estimation
No full textWe describe a simple method for making inference on a functional of a multivariate distri- bution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian MonteCarlo algorithm, where the proposed values of the functional of interest are weighed in terms of their em- pirical likelihood. This method is particularly useful when the “true” likelihood function associated with the working model is too costly to evaluate or when the working model is only partially specified
Jeffreys priors for mixture models
No full textMixture models may be a useful and flexible tool to describe data with
a complicated structure, for instance characterized by multimodality or asymmetry.
In a Bayesian setting, it is a well established fact that one need to be careful in using
improper prior distributions, since the posterior distribution may not be proper. This
feature leads to problems in carry out an objective Bayesian approach. In this work
an analysis of Jeffreys priors in the setting of finite mixture models will be presented
Approximate Bayesian computation for the elimination of nuisance parameters
No full textWe propose a novel use of the approximate Bayesian methodology. ABC
is a way to handle models for which the likelihood function may be considered
intractable; this situation is closely related to the problem of the elimination of nuisance
parameters: the model may contain a high-dimensional latent structure, so any
elaboration of the likelihood function could be difficult or even impossible when the
analysis is focused just on few parameters. We propose to use ABC to approximate
the likelihood function of the parameter of interest
Approximate Bayesian inference in semiparametric copula models
Full text linkWe describe a simple method for making inference on a functional of a multivariate distribution, based on its copula representation. We make use of an approximate Bayesian Monte Carlo algorithm, where the proposed values of the functional of interest are weighted in terms of their Bayesian exponentially tilted empirical likelihood. This method is particularly useful when the “true” likelihood function associated with the working model is too costly to evaluate or when the working model is only partially specified
Approximate Integrated Likelihood via ABC Methods
No full textWe propose a novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC is a way to handle models for which the likelihood function may be intractable or even unavailable and/or too costly to evaluate; in particular, we consider the problem of eliminating the nuisance parameters from a complex statistical model in order to produce a likelihood function depending on the quantity of interest only. Given a proper prior for the entire vector parameter, we propose to approximate the integrated likelihood by the ratio of kernel estimators of the marginal posterior and prior for the quantity of interest. We present several examples
On a loss-based prior for the number of components in mixture models
No full textWe introduce a prior distribution for the number of components of a mixture model. The
prior considers the worth of each possible mixture, measured by a loss function with
two components: one measures the loss in information in choosing the wrong mixture
and one the loss due to complexity
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