Abstract
In the application of discriminant analysis, a situation sometimes arises where individual measurements are screened by a multidimensional screening scheme. For this situation, a discriminant analysis with screened populations is considered from a Bayesian viewpoint, and an optimal predictive rule for the analysis is proposed. In order to establish a flexible method to incorporate the prior information of the screening mechanism, we propose a hierarchical screened scale mixture of normal (HSSMN) model, which makes provision for flexible modeling of the screened observations. An Markov chain Monte Carlo (MCMC) method using the Gibbs sampler and the Metropolis–Hastings algorithm within the Gibbs sampler is used to perform a Bayesian inference on the HSSMN models and to approximate the optimal predictive rule. A simulation study is given to demonstrate the performance of the proposed predictive discrimination procedure.
Highlights
The topic of analyzing multivariate screened data has received a great deal of attention over the last few decades
The first screening scheme may be defined by the q-dimensional region Cq of the random vector v0, so that only the students who satisfy v0 ∈ Cq can proceed to the admission process
According to these simulation results, we can say that the Markov chain Monte Carlo (MCMC) algorithm constructed in Section 3.3 provides an efficient method for estimating the screened scale mixture of normal (SSMN) distributions
Summary
The topic of analyzing multivariate screened data has received a great deal of attention over the last few decades. The screened data are generated from a non-normal joint distribution of v and v0 , having a multivariate screening scheme defined by a q-dimensional (q > 1) rectangle region Cq of v0. The first screening scheme may be defined by the q-dimensional region Cq of the random vector v0 (consisting of SAT scores, high-school GPA, and so on), so that only the students who satisfy v0 ∈ Cq can proceed to the admission process In this case, we encounter a crucial problem for applying the normal classification by [11]; given the screening scheme d v0 ∈ Cq , the assumption of the multivariate normal population distribution for [x| z = k] = [x| πk ], k = 1, 2, .
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