Mixtures of Shifted Asymmetric Laplace Distributions

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse Gaussian distribution. This approach is mathematically elegant and relatively computationally straightforward. Our novel mixture modelling approach is demonstrated on both simulated and real data to illustrate clustering and classification applications. In these analyses, our mixture of shifted asymmetric Laplace distributions performs favourably when compared to the popular Gaussian approach. This work, which marks an important step in the non-Gaussian model-based clustering and classification direction, concludes with discussion as well as suggestions for future work

Unsupervised Learning via Mixtures of Skewed Distributions with Hypercube Contours

Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace distributions. The component densities have two unique features: they include a multivariate weight function, and the marginal distributions are also asymmetric Laplace. We use these mixtures of multiple scaled shifted asymmetric Laplace distributions for clustering applications, but they could equally well be used in the supervised or semi-supervised paradigms. The expectation-maximization algorithm is used for parameter estimation and the Bayesian information criterion is used for model selection. Simulated and real data sets are used to illustrate the approach and, in some cases, to visualize the skewed hypercube structure of the components

Parsimonious Shifted Asymmetric Laplace Mixtures

A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An explicit two-stage parameter estimation procedure is described, and the Bayesian information criterion and the integrated completed likelihood are compared for model selection. This novel family of models is applied to real data, where it is compared to its Gaussian analogue within clustering and classification paradigms

The Co-occurrence of child and intimate partner maltreatment in the family: characteristics of the violent perpetrators

This study considers the characteristics associated with mothers and fathers who maltreat their child and each other in comparison to parents who only maltreat their child. One hundred and sixty-two parents who had allegations of child maltreatment made against them were considered. The sample consisted of 43 fathers (Paternal Family—PF) and 23 mothers (Maternal Family—MF) who perpetrated both partner and child maltreatment, together with 23 fathers (Paternal Child—PC) and 26 mothers (Maternal Child—MC) who perpetrated child maltreatment only. In addition, 2 fathers (Paternal Victim—PV) and 23 mothers (Maternal Victim—MV) were victims of intimate partner maltreatment and perpetrators of child maltreatment and 7 fathers (Paternal Non-abusive Carer—PNC) and 15 mothers (Maternal Non-abusive Carer—MNC) did not maltreat the child but lived with an individual who did. Within their family unit, 40.7% of parents perpetrated both intimate partner and child maltreatment. However, fathers were significantly more likely to maltreat both their partner and child than mothers and mothers were significantly more likely to be victims of intimate partner violence than fathers. PF fathers conducted the highest amount of physical and/or sexual child maltreatment while MC and MV mothers perpetrated the highest amount of child neglect. Few significant differences between mothers were found. PF fathers had significantly more factors associated with development of a criminogenic lifestyle than PC fathers. Marked sex differences were demonstrated with PF fathers demonstrating significantly more antisocial characteristics, less mental health problems and fewer feelings of isolation than MF mothers. MC mothers had significantly more childhood abuse, mental health problems, parenting risk factors and were significantly more likely to be biologically related to the child than PC fathers. This study suggests that violent families should be assessed and treated in a holistic manner, considering the effects of partner violence upon all family members, rather than exclusively intervening with the violent man

VLA 8.4-GHz monitoring observations of the CLASS gravitational lens B1933+503

The complex ten-component gravitational lens system B1933+503 has been monitored with the VLA during the period February to June 1998 with a view to measuring the time delay between the four compact components and hence to determine the Hubble parameter. Here we present the results of an `A' configuration 8.4-GHz monitoring campaign which consists of 37 epochs with an average spacing of 2.8 days. The data have yielded light curves for the four flat-spectrum radio components (components 1, 3, 4 and 6). We observe only small flux density changes in the four flat-spectrum components which we do not believe are predominantly intrinsic to the source. Therefore the variations do not allow us to determine the independent time delays in this system. However, the data do allow us to accurately determine the flux density ratios between the four flat-spectrum components. These will prove important as modelling constraints and could prove crucial in future monitoring observations should these data show only a monotonic increase or decrease in the flux densities of the flat-spectrum components.Comment: Accepted for publication in MNRAS. 5 pages, 2 included PostScript figure

The Cosmic Lens All-Sky Survey parent population - I. Sample selection and number counts

We present the selection of the Jodrell Bank Flat-spectrum (JBF) radio source sample, which is designed to reduce the uncertainties in the Cosmic Lens All-Sky Survey (CLASS) gravitational lensing statistics arising from the lack of knowledge about the parent population luminosity function. From observations at 4.86 GHz with the Very Large Array, we have selected a sample of 117 flat-spectrum radio sources with flux densities greater than 5 mJy. These sources were selected in a similar manner to the CLASS complete sample and are therefore representative of the parent population at low flux densities. The vast majority (~90 per cent) of the JBF sample are found to be compact on the arcsecond scales probed here and show little evidence of any extended radio jet emission. Using the JBF and CLASS complete samples we find the differential number counts slope of the parent population above and below the CLASS 30 mJy flux density limit to be -2.07+/-0.02 and -1.96+/-0.12, respectively.Comment: 10 pages, 4 figures, accepted for publication in MNRA

Keck spectroscopy of CLASS gravitational lenses

We present the optical spectra of four newly discovered gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS). These observations were carried out using the Low Resolution Imaging Spectrograph on the W. M. Keck-I Telescope as part of a program to study galaxy-scale gravitational lenses. From our spectra we found the redshift of the background source in CLASS B0128+437 (z_s=3.1240+-0.0042) and the lensing galaxy redshifts in CLASS B0445+123 (z_l=0.5583+-0.0003) and CLASS B0850+054 (z_l=0.5883+-0.0006). Intriguingly, we also discovered that CLASS B0631+519 may have two lensing galaxies (z_l,1=0.0896+-0.0001, z_l,2=0.6196+-0.0004). We also found a single unidentified emission line from the lensing galaxy in CLASS B0128+437 and the lensed source in CLASS B0850+054. We find the lensing galaxies in CLASS B0445+123 and CLASS B0631+519 (l,2) to be early-type galaxies with Einstein Radii of 2.8-3.0 h^{-1} kpc. The deflector in CLASS B0850+054 is a late-type galaxy with an Einstein Radius of 1.6 h^{-1} kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA

Lensing galaxies: light or dark?

In a recent paper, Hawkins (1997) argues on the basis of statistical studies of double-image gravitational lenses and lens candidates that a large population of dark lenses exists and that these outnumber galaxies with more normal mass-to-light ratios by a factor of 3:1. If correct, this is a very important result for many areas of astronomy including galaxy formation and cosmology. In this paper we discuss our new radio-selected gravitational lens sample, JVAS/CLASS, in order to test and constrain this proposition. We have obtained ground-based and HST images of all multiple-image lens systems in our sample and in 12 cases out of 12 we find the lensing galaxies in the optical and/or near infrared. Our success in finding lensing galaxies creates problems for the dark lens hypothesis. If it is to survive, ad hoc modifications seem to be necessary: only very massive galaxies (more than about one trillion solar masses) can be dark, and the cutoff in mass must be sharp. Our finding of lens galaxies in all the JVAS/CLASS systems is complementary evidence which supports the conclusion of Kochanek et al. (1997) that many of the wide-separation optically-selected pairs are physically distinct quasars rather than gravitational lens systems.Comment: 4 pages, 2 included figures, accepted for publication in Astronomy and Astrophysics. Paper version available on request. This replacement amends the text to allow more discussion of the overlap with astro-ph/971016

The channels of technology acquisition in commercial firms, and the NASA dissemination program

Technology acquisition in commercial firms, and NASA dissemination progra