Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery

This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data

Identification and separation of DNA mixtures using peak area information (Updated version of Statistical Research Paper No. 25)

We introduce a new methodology, based upon probabilistic expert systems, for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for ascertaining whether individuals, whose profiles have been measured, have contributed to the mixture, but also to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our probabilistic methodology is illustrated on case data examples and compared with alternative approaches. The advantages are that identification and separation issues can be handled in a unified way within a single probabilistic model and the uncertainty associated with the analysis is quantified. Further work, required to bring the methodology to a point where it could be applied to the routine analysis of casework, is discussed

Developmental toxic effects of ethylbenzene or toluene alone and in combination with butyl acetate in rats after inhalation exposure

First, the developmental toxic potential of n-butyl acetate (BA) was examined in Sprague-Dawley rats following whole body inhalation exposure, 6 h day-1, from day 6 to 20 of gestation, at concentrations of 0, 500, 1000, 2000 and 3000 ppm. Maternal toxicity was evidenced by significant decreases in body weight gain at 2000 and 3000 ppm, and by reduced food consumption at 1000 ppm and higher concentrations. The effects on prenatal development were limited to a significant decrease in fetal weight at 3000 ppm. Thus, inhaled BA was not a selective developmental toxicant. In the second part of this study, the developmental toxic effects of simultaneous exposures to ethylbenzene (EB) and BA, or to toluene (TOL) and BA were evaluated. Pregnant rats were administered EB (0, 250 or 1000 ppm) and BA (0, 500 or 1500 ppm), or TOL (0, 500 or 1500 ppm) and BA (0, 500, 1500 ppm), separately and in combinations, using a 2 × 2 factorial design. The maternal weight gain was reduced after exposure to 1000 ppm EB, to 1500 ppm BA, or to 1500 ppm TOL, either alone or in binary combinations. A significant reduction of fetal weight was associated with exposure to 1000 ppm EB alone, to either mixtures of EB with BA, or to 1500 ppm TOL alone or combined with BA at either concentration. No embryolethal or teratogenic effects were observed whatever the exposure. There was no evidence of interaction between EB and BA or between TOL and BA in causing maternal or developmental effects. Copyright © 2006 John Wiley & Sons, Ltd

Relabelling Algorithms for Large Dataset Mixture Models

Mixture models are flexible tools in density estimation and classification problems. Bayesian estimation of such models typically relies on sampling from the posterior distribution using Markov chain Monte Carlo. Label switching arises because the posterior is invariant to permutations of the component parameters. Methods for dealing with label switching have been studied fairly extensively in the literature, with the most popular approaches being those based on loss functions. However, many of these algorithms turn out to be too slow in practice, and can be infeasible as the size and dimension of the data grow. In this article, we review earlier solutions which can scale up well for large data sets, and compare their performances on simulated and real datasets. In addition, we propose a new, and computationally efficient algorithm based on a loss function interpretation, and show that it can scale up well in larger problems. We conclude with some discussions and recommendations of all the methods studied

Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas

<br>This paper presents a finite mixture of multivariate betas as a new model-based clustering method tailored to applications where the feature space is constrained to the unit hypercube. The mixture component densities are taken to be conditionally independent, univariate unimodal beta densities (from the subclass of reparameterized beta densities given by Bagnato and Punzo 2013). The EM algorithm used to fit this mixture is discussed in detail, and results from both this beta mixture model and the more standard Gaussian model-based clustering are presented for simulated skill mastery data from a common cognitive diagnosis model and for real data from the Assistment System online mathematics tutor (Feng et al 2009). The multivariate beta mixture appears to outperform the standard Gaussian model-based clustering approach, as would be expected on the constrained space. Fewer components are selected (by BIC-ICL) in the beta mixture than in the Gaussian mixture, and the resulting clusters seem more reasonable and interpretable.</br> <br>This article is in technical report form, the final publication is available at http://www.springerlink.com/openurl.asp?genre=article &id=doi:10.1007/s11634-013-0149-z</br&gt