On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression

In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood estimates of the regression coefficients do not exist. Gelman et al. (2008) recommended independent Cauchy distributions as default priors for the regression coefficients in logistic regression, even in the case of separation, and reported posterior modes in their analyses. As the mean does not exist for the Cauchy prior, a natural question is whether the posterior means of the regression coefficients exist under separation. We prove theorems that provide necessary and sufficient conditions for the existence of posterior means under independent Cauchy priors for the logit link and a general family of link functions, including the probit link. We also study the existence of posterior means under multivariate Cauchy priors. For full Bayesian inference, we develop a Gibbs sampler based on Polya-Gamma data augmentation to sample from the posterior distribution under independent Student-t priors including Cauchy priors, and provide a companion R package in the supplement. We demonstrate empirically that even when the posterior means of the regression coefficients exist under separation, the magnitude of the posterior samples for Cauchy priors may be unusually large, and the corresponding Gibbs sampler shows extremely slow mixing. While alternative algorithms such as the No-U-Turn Sampler in Stan can greatly improve mixing, in order to resolve the issue of extremely heavy tailed posteriors for Cauchy priors under separation, one would need to consider lighter tailed priors such as normal priors or Student-t priors with degrees of freedom larger than one

The reaction centre of the photounit of Rhodospirillum rubrum is anchored to the light-harvesting complex with four-fold rotational disorder

The minimal photounit of the photosynthetic membranes of the purple non-sulphur bacterium Rhodospirillum rubrum, comprising the reaction centre and the light-harvesting complex has been purified and crystallised in two dimensions in the presence of added phospholipids, and subsequently visualised by electron microscopy after negatively-staining. The position of the reaction centres within the light-harvesting ring has been determined at low resolution by the application of a new analysis for rotationally disordered identical units (here the reaction centres) within a two-dimensional crystalline lattice comprised of perfectly aligned unit cells (here the light-harvesting complexes). The reaction centre was found to preferentially occupy one of four orientations within the light-harvesting complex. The light-harvesting complex appears to be distorted to C4 symmetry, thus assuming a squarish shape when visualised by negative staining. A tentative structural model of the reaction centre-light-harvesting complex photounit which fits the experimental data is propose

Evaluation of serum paraoxonase, 1 and its association with serum cholinesterase as a cause of congenital anomalies

Background: Birth defects are conditions of prenatal origin that are present at birth, potentially impacting an infant's health, development, and/or survival. Several environmental toxins affect the growth of the fetus during the intrauterine period by affecting various cellular components. Pesticides and industrial chemicals are known toxins that can hinder the developmental process. In this study, authors are evaluating the relation of cholinesterase and paraoxonase-1 with visible congenital anomalies.Methods: Sixty babies delivered in the labor room were selected for the study. They were divided into two groups. Thirty newborns with visible congenital anomalies were included in Group I. Only babies with visible congenital anomalies were taken as inclusion criteria for this group. This group was compared with Group II, which were taken as controls and consisted of 30 healthy newborns without any congenital anomalies. Serum cholinesterase and serum paraoxonase-1 were estimated and statistical tests were applied.Results: Serum cholinesterase and serum paraoxonase-1 were significantly low in the babies with visible congenital anomalies. Serum cholinesterase levels showed a statistically significant positive correlation with serum paraoxonase 1 level in both the groups.Conclusions: Decrease in acetylcholinesterase by various environmental toxins and the associated decrease in serum paraoxonase level imposes significant oxidant stress and the resultant risk of developing congenital anomalies

Psychiatric morbidity and marital satisfaction: an empirical study on spouse of alcohol dependent cases in Barak valley, North-East India

Background: Alcohol dependence poses serious threats to the healthy functioning of the family apparatus in a multitude of ways. The deleterious impact of alcohol dependence on the couple remains an area of genuine concern for mental health professionals across the world.Methods: 69 cases were selected consecutively from the Psychiatry Outpatient department fulfilling the ICD-10 criteria of alcohol dependence syndrome and the spouse of these cases were assessed to evaluate the pattern and severity of psychiatric morbidity and marital satisfaction. Statistical associations were found between the important variables.Results: Out of the 69 cases, we found that mean age of the alcohol dependent cases was 40.75±8.21 while that of their spouse was 33.91±7.86 years Most of the alcoholics had 1-9 years of alcohol dependence (86.95%) and severe alcohol dependence (47.82%) based on SADD score. Majority of the spouse of the alcoholics suffered from psychiatric illness (60.86%) with the most common diagnosis being depressive disorder (30.43%) based on ICD-10 criteria. Most of the spouse had lower level of marital satisfaction and presence of marital dissatisfaction was significantly associated with a more severe dependence among their alcoholic husbands. Increased duration of alcohol consumption was associated with higher severity of alcohol dependence. Also, the presence of psychiatric morbidity in the spouse was associated with increased years and higher severity of alcohol dependence.Conclusions: If the spouses are psychologically healthy, a good support system is ensured for them which is necessary to maintain motivation levels to leave alcohol

ModuLand plug-in for Cytoscape: determination of hierarchical layers of overlapping network modules and community centrality

Summary: The ModuLand plug-in provides Cytoscape users an algorithm for determining extensively overlapping network modules. Moreover, it identifies several hierarchical layers of modules, where meta-nodes of the higher hierarchical layer represent modules of the lower layer. The tool assigns module cores, which predict the function of the whole module, and determines key nodes bridging two or multiple modules. The plug-in has a detailed JAVA-based graphical interface with various colouring options. The ModuLand tool can run on Windows, Linux, or Mac OS. We demonstrate its use on protein structure and metabolic networks. Availability: The plug-in and its user guide can be downloaded freely from: http://www.linkgroup.hu/modules.php. Contact: [email protected] Supplementary information: Supplementary information is available at Bioinformatics online.Comment: 39 pages, 1 figure and a Supplement with 9 figures and 10 table

Modeling the electron transport chain of purple non-sulfur bacteria

Purple non-sulfur bacteria (Rhodospirillaceae) have been extensively employed for studying principles of photosynthetic and respiratory electron transport phosphorylation and for investigating the regulation of gene expression in response to redox signals. Here, we use mathematical modeling to evaluate the steady-state behavior of the electron transport chain (ETC) in these bacteria under different environmental conditions. Elementary-modes analysis of a stoichiometric ETC model reveals nine operational modes. Most of them represent well-known functional states, however, two modes constitute reverse electron flow under respiratory conditions, which has been barely considered so far. We further present and analyze a kinetic model of the ETC in which rate laws of electron transfer steps are based on redox potential differences. Our model reproduces well-known phenomena of respiratory and photosynthetic operation of the ETC and also provides non-intuitive predictions. As one key result, model simulations demonstrate a stronger reduction of ubiquinone when switching from high-light to low-light conditions. This result is parameter insensitive and supports the hypothesis that the redox state of ubiquinone is a suitable signal for controlling photosynthetic gene expression