Bayesian analysis of mixture modelling using the multivariate t distribution

A finite mixture model using the multivariate t distribution has been shown as a robust extension of normal mixtures. In this paper, we present a Bayesian approach for inference about parameters of t-mixture models. The specifications of prior distributions are weakly informative to avoid causing nonintegrable posterior distributions. We present two efficient EM-type algorithms for computing the joint posterior mode with the observed data and an incomplete future vector as the sample. Markov chain Monte Carlo sampling schemes are also developed to obtain the target posterior distribution of parameters. The advantages of Bayesian approach over the maximum likelihood method are demonstrated via a set of real data.     

Inference for the measurement of poverty in the presence of a stochastic weighting variable

Empirical applications of poverty measurement often have to deal with a stochastic weighting variable such as household size. Within the framework of a bivariate distribution function defined over income and weight, I derive the limiting distributions of the decomposable poverty measures and of the ordinates of stochastic dominance curves. The poverty line is allowed to depend on the income distribution. It is shown how the results can be used to test hypotheses concerning changes in poverty. The inference procedures are briefly illustrated using Belgian data. An erratum to this article can be found at     

Multivariate distributions defined in terms of contours

The paper deals with the problem of using contours as the basis for defining probability distributions. First, the most general probability densities with given contours are obtained and the particular cases of circular and elliptical contours are dealt with. It is shown that the so-called elliptically contoured distributions do not include all possible cases. Next, the case of contours defined by polar coordinates is analyzed including its simulation and parameter estimation. Finally, the case of cumulative distribution functions with given contours is discussed. Several examples are used for illustrative purposes.     

Randomized response techniques for complex survey designs

Singh et al. ([13]) pointed out that the Randomized response (RR) technique proposed by Moors ([9]) is not desirable because it fails to protect the confidentiality of the respondents and they provided two alternative strategies free from the above drawback but limited to SRSWOR sampling only. In this paper, generalization of one of the strategies is provided for complex survey designs, wider class of estimators and for quantitative characteristics. Relative efficiency of the modified strategy is tested through empirical investigations. An erratum to this article is available at .     

Examples of the use of an equivalence theorem in constructing optimum experimental designs for random-effects nonlinear regression models

The problem considered is that of finding an optimum measurement schedule to estimate population parameters in a nonlinear model when the patient effects are random. The paper presents examples of the use of sensitivity functions, derived from the General Equivalence Theorem for D-optimality, in the construction of optimum population designs for such schedules. With independent observations, the theorem applies to the potential inclusion of a single observation. However, in population designs the observations are correlated and the theorem applies to the inclusion of an additional measurement schedule. In one example, three groups of patients of differing size are subject to distinct schedules. Numerical, as opposed to analytical, calculation of the sensitivity function is advocated. The required covariances of the observations are found by simulation.     

Form Perception of Partly Occluded Shapes in 4‐Month‐Old Infants

Two habituation experiments were conducted to investigate how 4‐month‐old infants perceive partly occluded shapes. In the first experiment, we presented a simple, partly occluded shape to the infants until habituation was reached. Then we showed either a probable completion (one that would be predicted on the basis of both local and global cues) or an improbable completion. Longer looking times were found for the improbably completed shape (compared to probable and control conditions), suggesting that the probable shape was perceived during partial occlusion. In the second experiment, infants were habituated to more ambiguous partly occluded shapes, where local and global cues would result in different completions. For adults, the percept of these shapes is usually dominated by global influences. However, after habituation the infants looked longer at the globally completed shapes. These results suggest that by the age of 4 months, infants are able to infer the perceptual completion of partly occluded shapes, but for more ambiguous shapes, this completion seems to be dominated by local influences.     

Framing Latina/o Immigration, Education, and Activism

Although Latinas/os have a long history in the USA and represent a growing percentage of the population, they remain largely invisible or stereotyped in dominant images and discourses. Such representations are often ahistorical, and they camouflage the effects of US power and inequality. However, the spring 2006 immigrant rights demonstrations disturbed dominant conceptions. The demonstrators called attention to the contradictory US practices that disrupt home countries, recruit labor migrants, and deny immigrants full participation. Likewise, the role of students in these demonstrations spurred reflections on why youth would walk out of their schools for immigrant rights. Inspired by these demonstrations, we combine materials from multiple disciplines to emphasize the significance of US imperialism, exploitation, and exclusion on Latina/o migration, education, and activism. Key to this article is a reframing of how the media, K-12 curriculum, and popular discourse often engage in a cultural cover-up that sustains inequality.     

Quadratic estimators of covariance components in a multivariate mixed linear model

It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist 39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model.