1,721,002 research outputs found
Applied Bayesian small-sample asymptotics: appli- cations in regression with continuous responses
No full textA note on the relationships between Bayesian and non-Bayesian predictive inference
No full textLet us consider a random vector Y distributed according to a statistical model depending on an unknown parameter vector. Suppose we are interested in prediction, where the object of inference is a future or a yet unobserved random variable X, not depending on Y. The aim of this contribution is to provide
some theoretical insight into the relationships between Bayesian and non-Bayesian higher-order asymptotic expansions for predictive densities. More precisely, we characterize prior probability distributionswhich guarantee the equivalence between
Bayesian asymptotic expansions of the predictive distribution and frequentist accurate refinements of the estimative predictive density. An illustration in the context of the scalar skew-normal model is discussed. As a further result, invoking asymptotic connections between adjustments of the profile likelihood and asymptotic expansions of predictive densities, we illustrate how Bayesian predictive densities allows for the construction of adjusted profile loglikelihoods
Default prior distributions from quasi- and quasi-profile likelihoods in the presence of nuisance parameters
No full textIn some problems of practical interest, a standard Bayesian analysis can be difficult to perform. This is true, for example, when the class of sampling parametric models is unknown or if robustness with respect to data or to model misspecifications is required. These situations can be usefully handled by using a posterior distribution for the parameter of interest which is based on a pseudo-likelihood function derived from estimating equations, i.e. on a quasi-likelihood, and on a suitable prior distribution.
The aim of this paper is to propose and discuss the construction of a default prior distribution for a scalar parameter of interest to be used together with a quasilikelihood function. We show that the proposed default prior can be interpreted as a
Jeffreys-type prior, since it is proportional to the square-root of the expected information derived from the quasi-likelihood. The frequentist coverage of the credible regions, based on the proposed procedure, is studied through Monte Carlo simulations
in the context of robustness theory and of generalized linear models with overdispersion
Bayesian composite marginal likelihoods
No full textThis paper proposes and discusses the use of composite marginal likelihoods for Bayesian inference. This approach allows one to deal with complex statistical models in the Bayesian framework, when the full likelihood - and thus the full posterior distribution - is impractical to compute or even analytically unknown.
The procedure is based on a suitable calibration of the composite likelihood
that yields the right asymptotic properties for the posterior probability distribution.
In this respect, an attractive technique is offered for important settings that at present are not easily tractable from a Bayesian perspective, such as, for instance, multivariate extreme value theory. Simulation studies and an application to multivariate extremes are analysed in detail
Robust likelihood functions in Bayesian inference
No full textIn order to deal with mild deviations from the assumed parametric model, we propose a procedure for accounting for model uncertainty in the Bayesian framework. In particular, in the derivation of posterior distributions, we discuss the use of robust pseudo-likelihoods, which offer the advantage of preventing the effects caused by model misspecifications, i.e. when the underlying distribution lies in a neighborhood of the assumed model. The influence functions of posterior summaries, such as the posterior mean, are investigated as well as the asymptotic properties of robust posterior distributions. Although the use of a pseudo-likelihood cannot be considered orthodox in the Bayesian perspective, it is shown that, also through some illustrative examples, how a robust pseudo-likelihood, with the same asymptotic properties of a genuine likelihood, can be useful in the inferential process in order to prevent the effects caused by model misspecifications
BAYESIAN COMPOSITE MARGINAL LIKELIHOODS
No full textThis paper proposes and discusses the use of composite marginal like-
lihoods for Bayesian inference. This approach allows one to deal with complex
statistical models in the Bayesian framework, when the full likelihood - and thus
the full posterior distribution - is impractical to compute or even analytically un-
known. The procedure is based on a suitable calibration of the composite likelihood
that yields the right asymptotic properties for the posterior probability distribu-
tion. In this respect, an attractive technique is offered for important settings that
at present are not easily tractable from a Bayesian perspective, such as, for in-
stance, multivariate extreme value theory. Simulation studies and an application
to multivariate extremes are analysed in detai
A matching prior for the shape parameter of the skew-normal distribution
No full textThis paper deals with the issue of performing a default Bayesian analysis on the shape parameter of the skew-normal distribution. Our approach is based on a suitable pseudo-likelihood function and a matching prior distribution for this parameter, when location (or regression) and scale parameters are unknown. This approach is important for both theoretical and practical reasons. From a theoretical perspective, it is shown that the proposed matching prior is proper thus inducing a proper posterior distribution for the shape parameter, also when the likelihood is monotone. From the practical perspective, the proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals
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