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Current understanding holds that financial contagion is driven mainly by system-wide interconnectedness of institutions. A distinction has been made between systematic and idiosyncratic channels of contagion, with shocks transmitted through the latter expected to be substantially more likely to lead to a crisis than through the former. Idiosyncratic connectivity is thought to be driven not simply by obviously shared characteristics among institutions, but more by the latent strategic position of firms in financial markets. We propose a Bayesian hierarchical model for multivariate financial time series that characterizes the interdependence in the idiosyncratic factors of a VAR model via a covariance graphical model whose structure is modeled through a latent position model. We develop an efficient algorithm that samples the network of the idiosyncratic factors and the latent positions underlying the network. We examine the dynamic volatility network and latent positions among 150 publicly listed institutions across the United States and Europe and how they contribute to systemic vulnerabilities and risk transmission.

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space ( Y , d ) . We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also cover the properties of the weighted cumulative Frechet mean. These tools allow us to derive several types of median inequalities for abstract metric spaces that hold for both negative and positive Alexandrov spaces. In particular, we show through an example that these bounds cannot be improved upon in general metric spaces. For weighted Frechet means, however, such inequalities can solely be derived for weights equal to or greater than one. This latter limitation highlights the inherent difficulties associated with abstract-valued random variables.

This study is the first to systematically investigate whether multiple child maltreatment is associated with HIV risk behaviors and adverse mental health outcomes among Asian-American women.We conducted a cross-sectional study of unmarried Chinese, Korean, and Vietnamese women (n = 400), aged 18 to 35, who are identified as children of immigrants, using computer-assisted survey interviews.Approximately 7 in 10 women reported having been maltreated as a child and 6.8% reported any type of sexual abuse. Only 15% of our sample reported having sex at age 16 or before, yet almost 60% had ever engaged with potentially risky sexual partners. Contrary to the findings from previous studies of White and Black women, sexual abuse plus other maltreatment was not associated with HIV risk behaviors among Asian-American women. However, it was associated with a marked increase in depression, lifetime suicidal ideation, and suicide attempts. A higher education level was associated with increased odds of HIV risk behaviors, including ever having had anal sex and ever having potentially risky sexual partners.There was no evidence indicating that multiple child maltreatment was linked with HIV risk behaviors, but it exhibited a robust association with poor mental health outcomes. These empirical patterns of internalizing trauma, suffering alone, and staying silent are in accord with Asian-cultural norms of saving face and maintaining family harmony. The prevention of multiple child maltreatment may reduce high levels of depression and suicidal behaviors in this population. It is urgent to identify victims of multiple child maltreatment and provide culturally appropriate interventions.

A minimum volume (MV) set, at level α, is a set Gα∗ having minimum volume among all those sets containing at least α probability mass. MV sets provide a natural notion of the ‘central mass’ of a distribution and, as such, have recently become popular as a tool for the detection of anomalies in multivariate data. Motivated by the fact that anomaly detection problems frequently arise in settings with temporally indexed measurements, we propose here a new method for the estimation of MV sets from dependent data. Our method is based on the concept of complexity-penalized estimation, extending recent work of Scott and Nowak for the case of independent and identically distributed measurements, and has both desirable theoretical properties and a practical implementation. Of particular note is the fact that, for a large class of stochastic processes, choice of an appropriate complexity penalty reduces to the selection of a single tuning parameter, which represents the data dependency of the underlying stochastic process. While in reality the dependence structure is unknown, we offer a data-dependent method for selecting this parameter, based on subsampling principles. Our work is motivated by and illustrated through an application to the detection of anomalous traffic levels in Internet traffic time series.

Vertex betweenness centrality is a metric that seeks to quantify a sense of the importance of a vertex in a network in terms of its ‘control’ on the flow of information along geodesic paths throughout the network. Two natural ways to extend vertex betweenness centrality to sets of vertices are (i) in terms of geodesic paths that pass through at least one of the vertices in the set, and (ii) in terms of geodesic paths that pass through all vertices in the set. The former was introduced by Everett and Borgatti [Everett, M., Borgatti, S., 1999. The centrality of groups and classes. Journal of Mathematical Sociology 23 (3), 181–201], and called group betweenness centrality. The latter, which we call co-betweenness centrality here, has not been considered formally in the literature until now, to the best of our knowledge. In this paper, we show that these two notions of centrality are in fact intimately related and, furthermore, that this relationship may be exploited to obtain deeper insight into both. In particular, we provide an expansion for group betweenness in terms of increasingly higher orders of co-betweenness, in a manner analogous to the Taylor series expansion of a mathematical function in calculus. We then demonstrate the utility of this expansion by using it to construct analytic lower and upper bounds for group betweenness that involve only simple combinations of (i) the betweenness of individual vertices in the group, and (ii) the co-betweenness of pairs of these vertices. Accordingly, we argue that the latter quantity, i.e., pairwise co-betweenness, is itself a fundamental quantity of some independent interest, and we present a computationally efficient algorithm for its calculation, which extends the algorithm of Brandes [Brandes, U., 2001. A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25, 163] in a natural manner. Applications are provided throughout, using a handful of different communication networks, which serve to illustrate the way in which our mathematical contributions allow for insight to be gained into the interaction of network structure, coalitions, and information flow in social networks.

Epilepsy - the world's most common serious brain disorder - is defined by recurrent unprovoked seizures that result from complex interactions between distributed neural populations. We explore some macroscopic characteristics of emergent ictal networks by considering intracranial recordings from human subjects with intractable epilepsy. For each seizure, we compute a simple measure of linear coupling between all electrode pairs (more than 2400) to define networks of interdependent electrodes during preictal and ictal time intervals. We analyze these networks by applying traditional measures from network analysis and identify statistically significant global and local changes in network topology. We find at seizure onset a diffuse breakdown in global coupling, and local changes indicative of increased throughput of specific cortical and subcortical regions. We conclude that network analysis yields measures to summarize the complicated coupling topology emergent at seizure onset. Using these measures, we can identify spatially localized brain regions that may facilitate seizures and may be potential targets for focal therapies.

Our interest in this paper is on the choice of spatial and categorical scale, and their interaction, in creating classifications of land cover from remotely sensed measurements. We note that in discussing categorical scale, the concept of spatial scale naturally arises, and in discussing spatial scale, the issue of aggregation of measurements must be considered. Therefore, and working towards an ultimate goal of producing multiscale, multigranular characterizations of land cover, we address here successively and in a cumulative fashion the topics of (1) aggregation of measurements across multiple scales, (2) adaptive choice of spatial scale, and (3) adaptive choice of categorical scale jointly with spatial scale. We show that the use of statistical finite mixture models with groups of original pixel-scale measurements, at successive spatial scales, offers improved pixel-wise classification accuracy as compared to the commonly used technique of label aggregation. We then show how a statistical model selection strategy may be used with the finite mixture models to provide a data-adaptive choice of spatial scale, varying by location (i.e., multiscale), from which classifications at least as accurate as those of any single spatial scale may be achieved. Finally, we extend this paradigm to allow for jointly adaptive selection of spatial and categorical scale. Our emphasis throughout is on the empirical quantification of the role of the various elements above, and a comparison of their performance with standard methods, using various artificial landscapes. The methods proposed in this paper should be useful for a variety of scale-related land cover classification tasks.

We consider the class of multiscale spatial process models introduced by Kolaczyk and Huang Geographical Analysis 33, (2001) 95–118. Recursive expressions are provided for the spatial covariance matrices generally, and a particularly simple closed-form expression is found to obtain for the corresponding eigenvalues for a sub-class of these processes.

Mixture analysis is a necessary component for capturing sub-pixel heterogeneity in the characterization of land cover from remotely sensed images. Mixture analysis approaches in remote sensing vary from conventional linear mixture models to nonlinear neural network mixture models. Linear mixture models are fairly simple and generally result in poor mixture analysis accuracy. Neural network models can achieve much higher accuracy, but typically lack interpretability. In this paper we present a mixture discriminant analysis (MDA) model for inferring land cover fractions within forest stands from Landsat Thematic Mapper images. Specifically, individual class distributions are modeled as mixtures of subclasses of Gaussian distributions, and land cover fractions are estimated using the corresponding posterior probabilities. Compared to a benchmark study on accuracy of mixture models with Plumas National Forest data, this MDA model easily outperforms traditional linear mixture models and parallels the performance of the ARTMAP neural network mixture model. In other words, the MDA model is observed to successfully combine the performance characteristics of more complex neural network models (due to the nonlinear nature of its classification rules), with the ease of interpretation associated with linear mixture models (due to its relatively simple structure). MDA models therefore offer an attractive alternative for addressing the mixture modeling problem in remote sensing.

We present quantitative statistical evidence for a $\gamma$-ray emission halo surrounding the Galaxy. Maps of the emission are derived. EGRET data were analyzed in a wavelet-based non-parametric hypothesis testing framework, using a model of expected diffuse (Galactic + isotropic) emission as a null hypothesis. The results show a statistically significant large scale halo surrounding the center of the Milky Way as seen from Earth. The halo flux at high latitudes is somewhat smaller than the isotropic gamma-ray flux at the same energy, though of the same order (O(10^(-7)--10^(-6)) ph/cm^2/s/sr above 1 GeV)., Comment: Final version accepted for publication in New Astronomy. Some additional results/discussion included, along with entirely revised figures. 19 pages, 15 figures, AASTeX. Better quality figs (PS and JPEG) are available at http://tigre.ucr.edu/halo/paper.html