Estimation of standard deviations and inverse-variance weights from an observed range

A variety of methods have been proposed to estimate a standard deviation, when only a sample range has been observed or reported. This problem occurs in the interpretation of individual clinical studies that are incompletely reported, and also in their incorporation into meta-analyses. The methods differ with respect to their focus being either on the standard deviation in the underlying population or on the particular sample in hand, a distinction that has not been widely recognized. In this article, we contrast and compare various estimators of these two quantities with respect to bias and mean squared error, for normally distributed data. We show that unbiased estimators are available for either quantity, and recommend our preferred methods. We also propose a Taylor series method to obtain inverse-variance weights, for samples where only the sample range is available; this method yields very little bias, even for quite small samples. In contrast, the naïve approach of simply taking the inverse of an estimated variance is shown to be substantially biased, and can place unduly large weight on small samples, such as small clinical trials in a meta-analysis. Accordingly, this naïve (but commonly used) method is not recommended.

Generalized and social anxiety disorder interactomes show distinctive overlaps with striosome and matrix interactomes

Mechanisms underlying anxiety disorders remain elusive despite the discovery of several associated genes. We constructed the protein-protein interaction networks (interactomes) of six anxiety disorders and noted enrichment for striatal expression among common genes in the interactomes. Five of these interactomes shared distinctive overlaps with the interactomes of genes that were differentially expressed in two striatal compartments (striosomes and matrix). Generalized anxiety disorder and social anxiety disorder interactomes showed exclusive and statistically significant overlaps with the striosome and matrix interactomes, respectively. Systematic gene expression analysis with the anxiety disorder interactomes constrained to contain only those genes that were shared with striatal compartment interactomes revealed a bifurcation among the disorders, which was influenced by the anterior cingulate cortex, nucleus accumbens, amygdala and hippocampus, and the dopaminergic signaling pathway. Our results indicate that the functionally distinct striatal pathways constituted by the striosome and the matrix may influence the etiological differentiation of various anxiety disorders.

Discrete Versions of Jensen-Fisher, Fisher and Bayes-Fisher Information Measures of Finite Mixture Distributions

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences.

On Cumulative Entropies in Terms of Moments of Order Statistics

In this paper, relations between some kinds of cumulative entropies and moments of order statistics are established. By using some characterizations and the symmetry of a non-negative and absolutely continuous random variable X, lower and upper bounds for entropies are obtained and illustrative examples are given. By the relations with the moments of order statistics, a method is shown to compute an estimate of cumulative entropies and an application to testing whether data are exponentially distributed is outlined.