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.

Multivariate genetic analysis of academic skills of the Queensland Core Skills Test and IQ highlight the importance of genetic g

This study examined the genetic and environmental relationships among 5 academic achievement skills of a standardized test of academic achievement, the Queensland Core Skills Test (QCST; Queensland Studies Authority, 2003a). QCST participants included 182 monozygotic pairs and 208 dizygotic pairs (mean 17 years +/- 0.4 standard deviation). IQ data were included in the analysis to correct for ascertainment bias. A genetic general factor explained virtually all genetic variance in the component academic skills scores, and accounted for 32% to 73% of their phenotypic variances. It also explained 56% and 42% of variation in Verbal IQ and Performance IQ respectively, suggesting that this factor is genetic g. Modest specific genetic effects were evident for achievement in mathematical problem solving and written expression. A single common factor adequately explained common environmental effects, which were also modest, and possibly due to assortative mating. The results suggest that general academic ability, derived from genetic influences and to a lesser extent common environmental influences, is the primary source of variation in component skills of the QCST.

Equational Reasoning as a Tool for Data Analysis

A combination of deductive reasoning, clustering, and inductive learning is given as an example of a hybrid system for exploratory data analysis. Visualization is replaced by a dialogue with the data.

Data analysis in multiple-frequency bioelectrical impedance analysis

The performance of three analytical methods for multiple-frequency bioelectrical impedance analysis (MFBIA) data was assessed. The methods were the established method of Cole and Cole, the newly proposed method of Siconolfi and co-workers and a modification of this procedure. Method performance was assessed from the adequacy of the curve fitting techniques, as judged by the correlation coefficient and standard error of the estimate, and the accuracy of the different methods in determining the theoretical values of impedance parameters describing a set of model electrical circuits. The experimental data were well fitted by all curve-fitting procedures (r = 0.9 with SEE 0.3 to 3.5% or better for most circuit-procedure combinations). Cole-Cole modelling provided the most accurate estimates of circuit impedance values, generally within 1-2% of the theoretical values, followed by the Siconolfi procedure using a sixth-order polynomial regression (1-6% variation). None of the methods, however, accurately estimated circuit parameters when the measured impedances were low (<20 Omega) reflecting the electronic limits of the impedance meter used. These data suggest that Cole-Cole modelling remains the preferred method for the analysis of MFBIA data.

Exploratory spatial data analysis techniques for examining urban crime

Regional planners, policy makers and policing agencies all recognize the importance of better understanding the dynamics of crime. Theoretical and application-oriented approaches which provide insights into why and where crimes take place are much sought after. Geographic information systems and spatial analysis techniques, in particular, are proving to be essential or studying criminal activity. However, the capabilities of these quantitative methods continue to evolve. This paper explores the use of geographic information systems and spatial analysis approaches for examining crime occurrence in Brisbane, Australia. The analysis highlights novel capabilities for the analysis of crime in urban regions.

Integrating technology to improve the efficiency of qualitative data analysis - A note on methods

Qualitative data analysis (QDA) is often a time-consuming and laborious process usually involving the management of large quantities of textual data. Recently developed computer programs offer great advances in the efficiency of the processes of QDA. In this paper we report on an innovative use of a combination of extant computer software technologies to further enhance and simplify QDA. Used in appropriate circumstances, we believe that this innovation greatly enhances the speed with which theoretical and descriptive ideas can be abstracted from rich, complex, and chaotic qualitative data. © 2001 Human Sciences Press, Inc.

Multivariate monitoring of a biological wastewater treatment process: a case study at Melbourne Water's Western Treatment Plant

Biological wastewater treatment is a complex, multivariate process, in which a number of physical and biological processes occur simultaneously. In this study, principal component analysis (PCA) and parallel factor analysis (PARAFAC) were used to profile and characterise Lagoon 115E, a multistage biological lagoon treatment system at Melbourne Water's Western Treatment Plant (WTP) in Melbourne, Australia. In this study, the objective was to increase our understanding of the multivariate processes taking place in the lagoon. The data used in the study span a 7-year period during which samples were collected as often as weekly from the ponds of Lagoon 115E and subjected to analysis. The resulting database, involving 19 chemical and physical variables, was studied using the multivariate data analysis methods PCA and PARAFAC. With these methods, alterations in the state of the wastewater due to intrinsic and extrinsic factors could be discerned. The methods were effective in illustrating and visually representing the complex purification stages and cyclic changes occurring along the lagoon system. The two methods proved complementary, with each having its own beneficial features. (C) 2003 Elsevier B.V. All rights reserved.

Multivariate genetic analysis of cognitive abilities in an adolescent twin sample

The sources of covariation among cognitive measures of Inspection Time, Choice Reaction Time, Delayed Response Speed and Accuracy, and IQ were examined in a classical twin design that included 245 monozygotic (MZ) and 298 dizygotic (DZ) twin pairs. Results indicated that a factor model comprising additive genetic and unique environmental effects was the most parsimonious. In this model, a general genetic cognitive factor emerged with factor loadings ranging from 0.28 to 0.64. Three other genetic factors explained the remaining genetic covariation between various speed and Delayed Response measures with IQ. However, a large proportion of the genetic variation in verbal (54%) and performance (25%) IQ was unrelated to these lower order cognitive measures. The independent genetic IQ variation may reflect information processes not captured by the elementary cognitive tasks, Inspection Time and Choice Reaction Time, nor our working memory task, Delayed Response. Unique environmental effects were mostly nonoverlapping, and partly represented test measurement error.

Flight data analysis of the HyShot 2 scramjet flight experiment

The development of scramjet propulsion for alternative launch and payload delivery capabilities has been composed largely of ground experiments for the last 40 years. With the goal of validating the use of short duration ground test facilities, a ballistic reentry vehicle experiment called HyShot was devised to achieve supersonic combustion in flight above Mach 7.5. It consisted of a double wedge intake and two back-to-back constant area combustors; one supplied with hydrogen fuel at an equivalence ratio of 0.34 and the other unfueled. Of the two flights conducted, HyShot 1 failed to reach the desired altitude due to booster failure, whereas HyShot 2 successfully accomplished both the desired trajectory and satisfactory scramjet operation. Postflight data analysis of HyShot 2 confirmed the presence of supersonic combustion during the approximately 3 s test window at altitudes between 35 and 29 km. Reasonable correlation between flight and some preflight shock tunnel tests was observed.