Bayesian Variations on the Frisch and Waugh Theme

The paper is devoted to discussing consequences of the so-called Frisch-Waugh Theorem to posterior inference and Bayesian model comparison. We adopt a generalised normal linear regression framework and weaken its assumptions in order to cover non-normal, jointly elliptical sampling distributions, autoregressive specifications, additional nuisance parameters and multi-equation SURE or VAR models. The main result is that inference based on the original full Bayesian model can be obtained using transformed data and reduced parameter spaces, provided the prior density for scale or precision parameters is appropriately modified.Bayesian inference, regression models, SURE models, VAR processes, data transformations

Robust bayesian inference in empirical regression models

Broadening the stochastic assumptions on the error terms of regression models was prompted by the analysis of linear multivariate t models in Zellner (1976). We consider a possible non-linear regression model under any multivariate elliptical data density, and examine Bayesian posterior and productive results. The latter are shown to be robust with respect to the specific choice of a sampling density within this elliptical class. In particular, sufficient conditions for such model robustness are that we single out a precision factor T2 on which we can specify an improper prior density. Apart from the posterior distribution of this nuisance parameter T 2, the entire analysis will then be completely unaffected by departures from Normality. Similar results hold in finite mixtures of such elliptical densities, which can be used to average out specification uncertainty

Bayesian marginal equivalence of elliptical regression models

Economics

Robust Bayesian inference in elliptical regression models

Bayesian Statistics

Posterior inference on long-run impulse responses

This paper describes a Bayesian analysis of impulse response functions. We show how many common priors imply that posterior densities for impulse responses at long horizons have no moments. Our results suggest that impulse responses should be assessed on the basis of their full posterior densities, and that standard estimates such as posterior means, variances or modes may be very misleading

A Bayesian analysis of exogeneity in models pooling time-series and cross-section data

Time Series

Robust Bayesian inference in Iq-Spherical models

The class of multivariate lq-spherical distributions is introduced and defined through their isodensity surfaces. We prove that, under a Jeffreys' type improper prior on the scale parameter, posterior inference on the location parameters is the same for all lq-spherical sampling models with common q. This gives us perfect inference robustness with respect to any departures from the reference case of independent sampling from the exponential power distribution

Semi-conjugate prior densities in multivariate t regression models

Regression Analysis

Robust Bayesian inference in Iq-Spherical models.

The class of multivariate lq-spherical distributions is introduced and defined through their isodensity surfaces. We prove that, under a Jeffreys' type improper prior on the scale parameter, posterior inference on the location parameters is the same for all lq-spherical sampling models with common q. This gives us perfect inference robustness with respect to any departures from the reference case of independent sampling from the exponential power distribution.Bayesian inference; Exponential power distributions; Inference robustness; lq-norm; Symmetric multivariate distributions;