Identified vector autoregressive (VAR) models have become widely used on time series data in recent years, but finite sample inference for such models remains a challenge. In this study, we propose a conjugate prior for Bayesian analysis of normalized VAR models. Under the prior, the marginal...

We propose a Bayesian stochastic search approach to selecting restrictions on multivariate regression models where the errors exhibit deterministic or stochastic conditional volatilities. We develop a Markov chain Monte Carlo (MCMC) algorithm that generates posterior restrictions on the...

In this paper, we study a special capture–recapture model, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$M_t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>M</mi> <mi>t</mi> </msub> </math> </EquationSource> </InlineEquation> model, using objective Bayesian methods. The challenge is to find a justified objective prior for an unknown population size <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>N</mi> </math> </EquationSource> </InlineEquation>. We develop an asymptotic objective prior for the discrete parameter <InlineEquation ID="IEq3"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Objective priors, especially reference priors, have been studied extensively for spatial data in the last decade. In this paper, we study objective priors for a CAR model. In particular, the properties of the reference prior and the corresponding posterior are studied. Furthermore, we show that...

The conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models both have been used extensively for the analysis of spatial structure underlying lattice data in many areas, such as epidemiology, demographics, economics, and geography. Default Bayesian analyses have been...

In this paper, the reference prior is developed for a truncated model with boundaries of support as two functions of an unknown parameter. It generalizes the result obtained in a recent paper by Berger et al. (2009), in which a rigorous definition of reference priors was proposed and the prior...

With sparse structures and conditional independence, one could estimate the precision matrix of Gaussian graphical models more efficiently. Sun and Sun (2005) studied objective priors for star-shape graphical models. We consider a generative star-shape model. Objective priors such as invariance...

This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development—such as the <italic>reference prior</italic> approach—often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain...

We propose a Bayesian stochastic search approach to selecting restrictions on multivariate regression models where the errors exhibit deterministic or stochastic conditional volatilities. We develop a Markov Chain Monte Carlo (MCMC) algorithm that generates posterior restrictions on the...