Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

A mixture model-based approach to the clustering of microarray expression data

Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets.

Estimating Two-Stage Models for Genetic Influences on Alcohol, Tobacco or Drug Use Initiation and Dependence Vulnerability in Twin and Family Data

Genetic research on risk of alcohol, tobacco or drug dependence must make allowance for the partial overlap of risk-factors for initiation of use, and risk-factors for dependence or other outcomes in users. Except in the extreme cases where genetic and environmental risk-factors for initiation and dependence overlap completely or are uncorrelated, there is no consensus about how best to estimate the magnitude of genetic or environmental correlations between Initiation and Dependence in twin and family data. We explore by computer simulation the biases to estimates of genetic and environmental parameters caused by model misspecification when Initiation can only be defined as a binary variable. For plausible simulated parameter values, the two-stage genetic models that we consider yield estimates of genetic and environmental variances for Dependence that, although biased, are not very discrepant from the true values. However, estimates of genetic (or environmental) correlations between Initiation and Dependence may be seriously biased, and may differ markedly under different two-stage models. Such estimates may have little credibility unless external data favor selection of one particular model. These problems can be avoided if Initiation can be assessed as a multiple-category variable (e.g. never versus early-onset versus later onset user), with at least two categories measurable in users at risk for dependence. Under these conditions, under certain distributional assumptions., recovery of simulated genetic and environmental correlations becomes possible, Illustrative application of the model to Australian twin data on smoking confirmed substantial heritability of smoking persistence (42%) with minimal overlap with genetic influences on initiation.

Occupational therapists' use and perceptions of written client education materials

OBJECTIVE. The purpose of this study was to examine occupational therapists' use and perceptions of written education materials for clients and the factors that therapists consider before distributing written materials to clients This study also aimed to determine whether use and perceptions of these materials differed for older clients METHOD. A random sample of 50 occupational therapists from Queensland, Australia, working in adult physical disabilities settings was surveyed with a structured questionnaire Data were analyzed descriptively and with nonparametric statistics RESULTS. Of 49 participants who used written materials, 54% had given them to more than halt of their last 10 clients, regardless of the clients' age Written materials, most often information sheets developed by the participants themselves; handwritten notes; and pamphlets were principally used to reinforce verbal information. Clients' cognitive abilities, primary language, communication skills, vision, and level of education most often were considered before distributing written materials Although participants generally were positive about the content and effectiveness of materials, ratings were significantly less positive related to older clients CONCLUSION. Client education was a core treatment modality for participants in this study, with written media most commonly being used to supplement verbal education Because participants were least positive about the effectiveness of written materials for older clients, further development of materials for this audience may be indicated.

Testing insect movement theory: empirical analysis of pest data routinely collected from agricultural crops

Observations of an insect's movement lead to theory on the insect's flight behaviour and the role of movement in the species' population dynamics. This theory leads to predictions of the way the population changes in time under different conditions. If a hypothesis on movement predicts a specific change in the population, then the hypothesis can be tested against observations of population change. Routine pest monitoring of agricultural crops provides a convenient source of data for studying movement into a region and among fields within a region. Examples of the use of statistical and computational methods for testing hypotheses with such data are presented. The types of questions that can be addressed with these methods and the limitations of pest monitoring data when used for this purpose are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Phase equilibrium data and liquidus for the system "MnO"-CaO-(Al2O3+SiO2) at Al2O3/SiO2 of 0.41

Phase-equilibrium data and the liquidus for the system. "MnO"-CaO-(Al2O3-SiO2) at a manganese-rich alloy saturation have been determined in the temperature range from 1423 to 1723 K. The results are presented in the form of a pseudoternary section "MnO"-CaO-(Al2O3 + SiO2) with an Al2O3/SiO2 weight ratio of 0.41. The following primary phases are present in the range of conditions investigated:, 3Al(2)O(3).2SiO(2); SiO2; MnO.Al2O3-2SiO(2); (Mn,Ca)O.SiO2; 2(Mn,Ca)O.SiO2; MnO.Al2O3; (Mn,Ca)O; alpha-2CaO.SiO2; alpha'-2CaO.SiO2; 2CaO.Al2O3.SiO2; CaO.SiO2, and CaO.Al2O3.2SiO(2). The presence of alumina in this system is shown to have a significant effect on the liquidus compared to the system "MnO"-CaO-SiO2, leading to, the stabilization of the anorthite and gehlenite phases.

Mineral chemistry, whole-rock compositions, and petrogenesis of leg 176 gabbros: Data and discussion

We report mineral chemistry, whole-rock major element compositions, and trace element analyses on Hole 735B samples drilled and selected during Leg 176. We discuss these data, together with Leg 176 shipboard data and Leg 118 sample data from the literature, in terms of primary igneous petrogenesis. Despite mineral compositional variation in a given sample, major constituent minerals in Hole 735B gabbroic rocks display good chemical equilibrium as shown by significant correlations among Mg# (= Mg/[Mg+Fe2+]) of olivine, clinopyroxene, and orthopyroxene and An (=Ca/[Ca+Na]) of plagioclase. This indicates that the mineral assemblages olivine + plagioclase in troctolite, plagioclase + clinopyroxene in gabbro, plagioclases + clinopyroxene + olivine in olivine gabbro, and plagioclase + clinopyroxene + olivine + orthopyroxene in gabbronorite, and so on, have all coprecipitated from their respective parental melts. Fe-Ti oxides (ilmenite and titanomagnetite), which are ubiquitous in most of these rocks, are not in chemical equilibrium with olivine, clinopyroxene, and plagioclase, but precipitated later at lower temperatures. Disseminated oxides in some samples may have precipitated from trapped Fe-Ti–rich melts. Oxides that concentrate along shear bands/zones may mark zones of melt coalescence/transport expelled from the cumulate sequence as a result of compaction or filter pressing. Bulk Hole 735B is of cumulate composition. The most primitive olivine, with Fo = 0.842, in Hole 735B suggests that the most primitive melt parental to Hole 735B lithologies must have Mg# ≤ 0.637, which is significantly less than Mg# = 0.714 of bulk Hole 735B.

Alcohol, tobacco and breast cancer - collaborative reanalysis of individual data from 53 epidemiological studies, including 58 515 women with breast cancer and 95 067 women without the disease

Alcohol and tobacco consumption are closely correlated and published results on their association with breast cancer have not always allowed adequately for confounding between these exposures. Over 80% of the relevant information worldwide on alcohol and tobacco consumption and breast cancer were collated, checked and analysed centrally. Analyses included 58515 women with invasive breast cancer and 95067 controls from 53 studies. Relative risks of breast cancer were estimated, after stratifying by study, age, parity and, where appropriate, women's age when their first child was born and consumption of alcohol and tobacco. The average consumption of alcohol reported by controls from developed countries was 6.0 g per day, i.e. about half a unit/drink of alcohol per day, and was greater in ever-smokers than never-smokers, (8.4 g per day and 5.0 g per day, respectively). Compared with women who reported drinking no alcohol, the relative risk of breast cancer was 1.32 (1.19 - 1.45, P < 0.00001) for an intake of 35 - 44 g per day alcohol, and 1.46 (1.33 - 1.61, P < 0.00001) for greater than or equal to 45 g per day alcohol. The relative risk of breast cancer increased by 7.1% (95% CI 5.5-8.7%; P