Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models

In this paper, we propose novel methods of quantifying expert opinion about prior distributions for multinomial models. Two different multivariate priors are elicited using median and quartile assessments of the multinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution, as a tractable conjugate prior, from those of the univariate betas through various forms of reconciliation using least-squares techniques. However, a multivariate copula function will give a more flexible correlation structure between multinomial parameters if it is used as their multivariate prior distribution. So, second, we use beta marginal distributions to construct a Gaussian copula as a multivariate normal distribution function that binds these marginals and expresses the dependence structure between them. The proposed method elicits a positive-definite correlation matrix of this Gaussian copula. The two proposed methods are designed to be used through interactive graphical software written in Java

The Staphylococcus aureus Response to Unsaturated Long Chain Free Fatty Acids: Survival Mechanisms and Virulence Implications

Staphylococcus aureus is an important human commensal and opportunistic pathogen responsible for a wide range of infections. Long chain unsaturated free fatty acids represent a barrier to colonisation and infection by S. aureus and act as an antimicrobial component of the innate immune system where they are found on epithelial surfaces and in abscesses. Despite many contradictory reports, the precise anti-staphylococcal mode of action of free fatty acids remains undetermined. In this study, transcriptional (microarrays and qRT-PCR) and translational (proteomics) analyses were applied to ascertain the response of S. aureus to a range of free fatty acids. An increase in expression of the σB and CtsR stress response regulons was observed. This included increased expression of genes associated with staphyloxanthin synthesis, which has been linked to membrane stabilisation. Similarly, up-regulation of genes involved in capsule formation was recorded as were significant changes in the expression of genes associated with peptidoglycan synthesis and regulation. Overall, alterations were recorded predominantly in pathways involved in cellular energetics. In addition, sensitivity to linoleic acid of a range of defined (sigB, arcA, sasF, sarA, agr, crtM) and transposon-derived mutants (vraE, SAR2632) was determined. Taken together, these data indicate a common mode of action for long chain unsaturated fatty acids that involves disruption of the cell membrane, leading to interference with energy production within the bacterial cell. Contrary to data reported for other strains, the clinically important EMRSA-16 strain MRSA252 used in this study showed an increase in expression of the important virulence regulator RNAIII following all of the treatment conditions tested. An adaptive response by S. aureus of reducing cell surface hydrophobicity was also observed. Two fatty acid sensitive mutants created during this study were also shown to diplay altered pathogenesis as assessed by a murine arthritis model. Differences in the prevalence and clinical importance of S. aureus strains might partly be explained by their responses to antimicrobial fatty acids

Hierarchies of Archimedean copulas

We present a flexible class of hierarchical copulas capable of modelling multidimensional joint distributions of asset returns with a richer rank correlation structure than existing models. We derive estimators and simulation techniques. The methods are applied to an illustrative portfolio consisting of a subset of DAX stocks.Copulas, Portfolio management, Risk management, Insurance mathematics,

An empirical analysis of multivariate copula models

Since the pioneering work of Embrechts and co-authors in 1999, copula models have enjoyed steadily increasing popularity in finance. Whereas copulas are well studied in the bivariate case, the higher-dimensional case still offers several open issues and it is far from clear how to construct copulas which sufficiently capture the characteristics of financial returns. For this reason, elliptical copulas (i.e. Gaussian and Student-t copula) still dominate both empirical and practical applications. On the other hand, several attractive construction schemes have appeared in the recent literature promising flexible but still manageable dependence models. The aim of this work is to empirically investigate whether these models are really capable of outperforming its benchmark, i.e. the Student-t copula and, in addition, to compare the fit of these different copula classes among themselves.KS-copula, Hierarchical Archimedian, Product copulas, Pair-copula decomposition,

Copula-Based Measures of Association

none1Measure of association is a broad term that denotes the class of all the measures that have been constructed with the aim of quantifying specific relationships between two or more variables. Measures of association based on copulas are invariant with respect to the univariate marginal distributions. These measures are able to capture positive as well as negative association and they do not alter the value in case of strictly increasing transformations of the variables.mixedMarta Nai RusconeNAI RUSCONE, Mart