The Overlooked Potential of Generalized Linear Models in Astronomy - I: Binomial Regression

Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -- the first in a series aimed at illustrating the power of these methods in astronomical applications -- we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity $\approx 1.3 \times 10^{-4} Z_{\bigodot}$, an increase of $1.2 \times 10^{-2}$ in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.Comment: 20 pages, 10 figures, 3 tables, accepted for publication in Astronomy and Computin

The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations

In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster population $N_{\rm GC}$ is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between $N_{\rm GC}$ and the following galaxy properties: central black hole mass, dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude. The methodology introduced herein naturally accounts for heteroscedasticity, intrinsic scatter, errors in measurements in both axes (either discrete or continuous), and allows modelling the population of globular clusters on their natural scale as a non-negative integer variable. Prediction intervals of 99% around the trend for expected $N_{\rm GC}$comfortably envelope the data, notably including the Milky Way, which has hitherto been considered a problematic outlier. Finally, we demonstrate how random intercept models can incorporate information of each particular galaxy morphological type. Bayesian variable selection methodology allows for automatically identifying galaxy types with different productions of GCs, suggesting that on average S0 galaxies have a GC population 35% smaller than other types with similar brightness.Comment: 14 pages, 12 figures. Accepted for publication in MNRA

Optima Nutrition: an allocative efficiency tool to reduce childhood stunting by better targeting of nutrition-related interventions

Published online: 20 March 2018Background: Child stunting due to chronic malnutrition is a major problem in low- and middle-income countries due, in part, to inadequate nutrition-related practices and insufficient access to services. Limited budgets for nutritional interventions mean that available resources must be targeted in the most cost-effective manner to have the greatest impact. Quantitative tools can help guide budget allocation decisions. Methods: The Optima approach is an established framework to conduct resource allocation optimization analyses. We applied this approach to develop a new tool, ‘Optima Nutrition’, for conducting allocative efficiency analyses that address childhood stunting. At the core of the Optima approach is an epidemiological model for assessing the burden of disease; we use an adapted version of the Lives Saved Tool (LiST). Six nutritional interventions have been included in the first release of the tool: antenatal micronutrient supplementation, balanced energy-protein supplementation, exclusive breastfeeding promotion, promotion of improved infant and young child feeding (IYCF) practices, public provision of complementary foods, and vitamin A supplementation. To demonstrate the use of this tool, we applied it to evaluate the optimal allocation of resources in 7 districts in Bangladesh, using both publicly available data (such as through DHS) and data from a complementary costing study. Results: Optima Nutrition can be used to estimate how to target resources to improve nutrition outcomes. Specifically, for the Bangladesh example, despite only limited nutrition-related funding available (an estimated $0.75 per person in need per year), even without any extra resources, better targeting of investments in nutrition programming could increase the cumulative number of children living without stunting by 1.3 million (an extra 5%) by 2030 compared to the current resource allocation. To minimize stunting, priority interventions should include promotion of improved IYCF practices as well as vitamin A supplementation. Once these programs are adequately funded, the public provision of complementary foods should be funded as the next priority. Programmatic efforts should give greatest emphasis to the regions of Dhaka and Chittagong, which have the greatest number of stunted children. Conclusions: A resource optimization tool can provide important guidance for targeting nutrition investments to achieve greater impact.Ruth Pearson, Madhura Killedar, Janka Petravic, Jakub J. Kakietek, Nick Scott, Kelsey L. Grantham, Robyn M. Stuart, David J. Kedziora, Cliff C. Kerr, Jolene Skordis-Worrall, Meera Shekar and David P. Wilso

Chameleonic Generalized Brans--Dicke model and late-time acceleration

In this paper we consider Chameleonic Generalized Brans--Dicke Cosmology in the framework of FRW universes. The bouncing solution and phantom crossing is investigated for the model. Two independent cosmological tests: Cosmological Redshift Drift (CRD) and distance modulus are applied to test the model with the observation.Comment: 20 pages, 15 figures, to be published in Astrophys. Space Sci. (2011

Gravitational Lensing with Three-Dimensional Ray Tracing

High redshift sources suffer from magnification or demagnification due to weak gravitational lensing by large scale structure. One consequence of this is that the distance-redshift relation, in wide use for cosmological tests, suffers lensing-induced scatter which can be quantified by the magnification probability distribution. Predicting this distribution generally requires a method for ray-tracing through cosmological N-body simulations. However, standard methods tend to apply the multiple thin-lens approximation. In an effort to quantify the accuracy of these methods, we develop an innovative code that performs ray-tracing without the use of this approximation. The efficiency and accuracy of this computationally challenging approach can be improved by careful choices of numerical parameters; therefore, the results are analysed for the behaviour of the ray-tracing code in the vicinity of Schwarzschild and Navarro-Frenk-White lenses. Preliminary comparisons are drawn with the multiple lens-plane ray-bundle method in the context of cosmological mass distributions for a source redshift of $z_{s}=0.5$.Comment: 17 pages, 10 figures, 0 tables; Accepted for publication in MNRA

Dysregulation of Gene Expression in a Lysosomal Storage Disease Varies between Brain Regions Implicating Unexpected Mechanisms of Neuropathology

The characteristic neurological feature of many neurogenetic diseases is intellectual disability. Although specific neuropathological features have been described, the mechanisms by which specific gene defects lead to cognitive impairment remain obscure. To gain insight into abnormal functions occurring secondary to a single gene defect, whole transcriptome analysis was used to identify molecular and cellular pathways that are dysregulated in the brain in a mouse model of a lysosomal storage disorder (LSD) (mucopolysaccharidosis [MPS] VII). We assayed multiple anatomical regions separately, in a large cohort of normal and diseased mice, which greatly increased the number of significant changes that could be detected compared to past studies in LSD models. We found that patterns of aberrant gene expression and involvement of multiple molecular and cellular systems varied significantly between brain regions. A number of changes revealed unexpected system and process alterations, such as up-regulation of the immune system with few inflammatory changes (a significant difference from the closely related MPS IIIb model), down-regulation of major oligodendrocyte genes even though white matter changes are not a feature histopathologically, and a plethora of developmental gene changes. The involvement of multiple neural systems indicates that the mechanisms of neuropathology in this type of disease are much broader than previously appreciated. In addition, the variation in gene dysregulation between brain regions indicates that different neuropathologic mechanisms may predominate within different regions of a diseased brain caused by a single gene mutation

Genome-wide association studies of cancer: current insights and future perspectives.

Genome-wide association studies (GWAS) provide an agnostic approach for investigating the genetic basis of complex diseases. In oncology, GWAS of nearly all common malignancies have been performed, and over 450 genetic variants associated with increased risks have been identified. As well as revealing novel pathways important in carcinogenesis, these studies have shown that common genetic variation contributes substantially to the heritable risk of many common cancers. The clinical application of GWAS is starting to provide opportunities for drug discovery and repositioning as well as for cancer prevention. However, deciphering the functional and biological basis of associations is challenging and is in part a barrier to fully unlocking the potential of GWAS

Relationship in fluoride adsorption on fish-bone charcoal

157-162<span style="font-size:11.0pt;line-height:115%; font-family:" calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-fareast-font-family:="" "times="" new="" roman";mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:="" minor-latin;mso-bidi-font-family:arial;mso-ansi-language:en-us;mso-fareast-language:="" en-us;mso-bidi-language:ar-sa"="">Batch adsorption studies have been conducted to determine the effects of some parameters such as contact time, initial solute concentration and dose of adsorbent on the adsorption of fluoride on the fish-bone charcoal. To simulate field conditions, the test fluoride solutions of different concentrations are prepared by using the tap water. The percentage fluoride removal is found to be function of the dose of adsorbent and time at a given initial concentration. Empirical relationship has been attempted to predict the percentage fluoride removal at any time for known values of dose of adsorbent and initial solute concentration under observed test conditions.</span

Defluoridation and empirical models in column studies using fishbone charcoal

237-244<span style="font-size:11.0pt;mso-bidi-font-size:10.0pt; line-height:115%;font-family:" calibri","sans-serif";mso-ascii-theme-font:minor-latin;="" mso-fareast-font-family:"times="" new="" roman";mso-fareast-theme-font:minor-fareast;="" mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"times="" roman";="" mso-ansi-language:en-us;mso-fareast-language:en-us;mso-bidi-language:ar-sa"="">Column bed adsorption studies have been carried out to study the fluoride removal on fishbone charcoal, and to determine the effects of the various operating variables. The useful (or effective) treated effluent volume (corresponding to the desired breakthrough concentration of 1.0 mg/L of fluoride) is found to be a function of the effluent flow rate, initial solute concentration and column bed depth. The useful treated effluent volume decreased with an increase in the flow rate and initial fluoride concentration, but it increased with the column bed depth. Empirical relationships have been developed to predict the stated useful treated effluent volume for the known values of flow rate, column bed depth and initial fluoride concentration for the observed test conditions. The relationships evolved manifest high correlation coefficients. The studies are useful in small installations.</span