Subjective Bayesian Analysis of the Elliptical Model

Abstract

The multivariate elliptical model is considered, such as to derive subjective Bayesian estimators of the location vector and some functions of the characteristic matrix for the normal-inverse Wishart prior and the normal-Wishart prior which was considered by Bekker and Roux (1995). Fang and Li (1999) considered the elliptical model for Bayesian analysis but with an objective prior structure.

A gamma-mixture class of distributions with Bayesian application

“…similar to the results of [7] where K ν (.) is the Bessel function of the third kind defined by Eq.3.478(4), p.370 of [10].…”

“…This is supported by Table 1. From Table 1 and Figure 5, the results of [3] and [7] are again apparent regarding the better performance of the gamma prior when compared to the inverse-gamma prior. The marginal posterior density function (6) for the hypergeometric gamma prior, with p = 1 and q = 1, of σ 2 for the 100 different samples can be viewed in Figure 6.…”

“…The genesis for this paper followed from the performance study done by [7] to evaluate the subjective normal-gamma and normal-inverse gamma distributions as possible priors for the parameters of the normal model. It was demonstrated by comparing different measures for a simulated as well as a real dataset that the non-conjugate mathematically intractable normal-gamma is a suitable competitor for the conjugate normal-inverse gamma prior.…”

Wishart distributions: Advances in theory with Bayesian application

“…Wishart and hypergeometric Wishart distributions, i.e., Σ Σ Σ Posterior samples of size 10,000 are simulated using a Gibbs sampling scheme with an additional Metropolis-Hastings algorithm [15], adapted from [29,30].…”