Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models

Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where a graph means the configuration of nonzero offdiagonal elements in the inverse of the covariance matrix. Our prior for the covariance matrix is such that the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We give empirical results that show the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix. The advantage is greatest when the number of observations is small relative to the dimension of the covariance matrix. The article also shows empirically that there is minimal change in statistical efficiency in using the mixture over decomposable graphs prior for estimating a general covariance compared to the Bayesian estimator by Wong et al. (2003), even when the graph of the covariance matrix is nondecomposable. However, our approach has some important advantages over that of Wong et al. (2003). Our method requires the number of decomposable graphs for each graph size. We show how to estimate these numbers using simulation and that the simulation results agree with analytic results when such results are known. We also show how to estimate the posterior distribution of the covariance matrix using Markov chain Monte Carlo with the elements of the covariance matrix integrated out and give empirical results that show the sampler is computationally efficient and converges rapidly. Finally, we note that both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.Covariance selection; Graphical models; Reduced conditional sampling; Variable selection

Characterization of three vasopressin receptor 2 variants: an apparent polymorphism (V266A) and two loss-of-function mutations (R181C and M311V).

Arginine vasopressin (AVP) is released from the posterior pituitary and controls water homeostasis. AVP binding to vasopressin V2 receptors (V2Rs) located on kidney collecting duct epithelial cells triggers activation of Gs proteins, leading to increased cAMP levels, trafficking of aquaporin-2 water channels, and consequent increased water permeability and antidiuresis. Typically, loss-of-function V2R mutations cause nephrogenic diabetes insipidus (NDI), whereas gain-of-function mutations cause nephrogenic syndrome of inappropriate antidiuresis (NSIAD). Here we provide further characterization of two mutant V2Rs, R181C and M311V, reported to cause complete and partial NDI respectively, together with a V266A variant, in a patient diagnosed with NSIAD. Our data in HEK293FT cells revealed that for cAMP accumulation, AVP was about 500- or 30-fold less potent at the R181C and M311V mutants than at the wild-type receptor respectively (and about 4000- and 60-fold in COS7 cells respectively). However, in contrast to wild type V2R, the R181C mutant failed to increase inositol phosphate production, while with the M311V mutant, AVP exhibited only partial agonism in addition to a 37-fold potency decrease. Similar responses were detected in a BRET assay for β-arrestin recruitment, with the R181C receptor unresponsive to AVP, and partial agonism with a 23-fold decrease in potency observed with M311V in both HEK293FT and COS7 cells. Notably, the V266A V2R appeared functionally identical to the wild-type receptor in all assays tested, including cAMP and inositol phosphate accumulation, β-arrestin interaction, and in a BRET assay of receptor ubiquitination. Each receptor was expressed at comparable levels. Hence, the M311V V2R retains greater activity than the R181C mutant, consistent with the milder phenotype of NDI associated with this mutant. Notably, the R181C mutant appears to be a Gs protein-biased receptor incapable of signaling to inositol phosphate or recruiting β-arrestin. The etiology of NSIAD in the patient with V266A V2R remains unknown

2022 Playful Gardens Report

Playful Gardens is a monthly inclusive family day held within the Dundee Botanic gardens. It’s key aims are to offer relaxed outdoor opportunities to play creatively together and access support, for families who may face additional challenges in other environments. This report brings together the evaluation of the Pilot in 2022

2022 Playful Gardens Report

Playful Gardens is a monthly inclusive family day held within the Dundee Botanic gardens. It’s key aims are to offer relaxed outdoor opportunities to play creatively together and access support, for families who may face additional challenges in other environments. This report brings together the evaluation of the Pilot in 2022

Adding Adhesion to a Chemical Signaling Model for Somite Formation

Somites are condensations of mesodermal cells that form along the two sides of the neural tube during early vertebrate development. They are one of the first instances of a periodic pattern, and give rise to repeated structures such as the vertebrae. A number of theories for the mechanisms underpinning somite formation have been proposed. For example, in the “clock and wavefront” model (Cooke and Zeeman in J. Theor. Biol. 58:455– 476, 1976), a cellular oscillator coupled to a determination wave progressing along the anterior-posterior axis serves to group cells into a presumptive somite. More recently, a chemical signaling model has been developed and analyzed by Maini and coworkers (Collier et al. in J. Theor. Biol. 207:305–316, 2000; Schnell et al. in C. R. Biol. 325:179– 189, 2002; McInerney et al. in Math. Med. Biol. 21:85–113, 2004), with equations for two chemical regulators with entrained dynamics. One of the chemicals is identified as a somitic factor, which is assumed to translate into a pattern of cellular aggregations via its effect on cell–cell adhesion. Here, the authors propose an extension to this model that includes an explicit equation for an adhesive cell population. They represent cell adhesion via an integral over the sensing region of the cell, based on a model developed previousl

Impediments of Labor Contracts on Prison Administrators’ Response to Staff–Inmate Sexual Misconduct

Sexual violence in adult correctional facilities led to the enactment of the 2003 Prison Rape Elimination Act as one approach to reducing this form of institutional violence. The current study examined collective bargaining agreements governing correctional agencies to identify impediments that may impact administrators’ responses to sexual violence, specifically in instances of allegations of staff–inmate sexual misconduct. In addition, structured interviews and focus groups with correctional administrators and labor representatives were used to develop policy recommendations. Contract language and interview participants demonstrated that a myriad of cultural and structural characteristics of prisons as well as pragmatic considerations may serve to inhibit the implementation of some policy changes. Interview participants identified several insights about contemporary prison settings and modifications that may aid in reducing some forms of institutional violence