Limit laws for random vectors with an extreme component

Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation provides a rich description of extremal dependence in the case of asymptotic dependence, but fails to distinguish between exact independence and asymptotic independence. Hidden regular variation addresses this problem by requiring components of the random vector to be simultaneously large but on a smaller scale than the scale for the marginal distributions. In doing so, hidden regular variation typically restricts attention to that part of the probability space where all variables are simultaneously large. However, since under asymptotic independence the largest values do not occur in the same observation, the region where variables are simultaneously large may not be of primary interest. A different philosophy was offered in the paper of Heffernan and Tawn [J. R. Stat. Soc. Ser. B Stat. Methodol. 66 (2004) 497--546] which allows examination of distributional tails other than the joint tail. This approach used an asymptotic argument which conditions on one component of the random vector and finds the limiting conditional distribution of the remaining components as the conditioning variable becomes large. In this paper, we provide a thorough mathematical examination of the limiting arguments building on the orientation of Heffernan and Tawn [J. R. Stat. Soc. Ser. B Stat. Methodol. 66 (2004) 497--546]. We examine the conditions required for the assumptions made by the conditioning approach to hold, and highlight simililarities and differences between the new and established methods.Comment: Published at http://dx.doi.org/10.1214/105051606000000835 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Movement of Economics Professors among Top Research Universities in the US

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Utilization of CT scanning associated with complex spine surgery.

BackgroundDue to the risk associated with exposure to ionizing radiation, there is an urgent need to identify areas of CT scanning overutilization. While increased use of diagnostic spinal imaging has been documented, no previous research has estimated the magnitude of follow-up imaging used to evaluate the postoperative spine.MethodsThis retrospective cohort study quantifies the association between spinal surgery and CT utilization. An insurance database (Humana, Inc.) with ≈ 19 million enrollees was employed, representing 8 consecutive years (2007-2014). Surgical and imaging procedures were captured by anatomic-specific CPT codes. Complex surgeries included all cervical, thoracic and lumbar instrumented spine fusions. Simple surgeries included discectomy and laminectomy. Imaging was restricted to CT and MRI. Postoperative imaging frequency extended to 5-years post-surgery.ResultsThere were 140,660 complex spinal procedures and 39,943 discectomies and 49,889 laminectomies. MRI was the predominate preoperative imaging modality for all surgical procedures (median: 80%; range: 73-82%). Postoperatively, CT prevalence following complex procedures increased more than two-fold from 6 months (18%) to 5 years (≥40%), and patients having a postoperative CT averaged two scans. For simple procedures, the prevalence of postoperative CT scanning never exceeded 30%.ConclusionsCT scanning is used frequently for follow-up imaging evaluation following complex spine surgery. There is emerging evidence of an increased cancer risk due to ionizing radiation exposure with CT. In the setting of complex spine surgery, actions to mitigate this risk should be considered and include reducing nonessential scans, using the lowest possible radiation dose protocols, exerting greater selectivity in monitoring the developing fusion construct, and adopting non-ferromagnetic implant biomaterials that facilitate MRI postoperatively

Advance directives in home health and hospice agencies: United States, 2007

This report provides nationally representative data on policies, storage, and implementation of advance directives (ADs) in home health and hospice (HHH) agencies in the United States using the National Home and Hospice Care Survey. Federally mandated ADs policies were followed in >93% of all agencies. Nearly all agencies stored ADs in a file at the agency, but only half stored them at the patient's residence. Nearly all agencies informed staff about the AD, but only 77% and 72% of home health agencies informed the attending physician and next-of-kin, respectively. Home health and hospice agencies are nearly universally compliant with ADs policies that are required in order to receive Medicare and Medicaid payments, but have much lower rates of adoption of ADs policies beyond federally mandated minimums

Online Reputation Systems in Web 2.0 Era

Web 2.0 has transformed how reputation systems are designed and used by the Web. Based on a thorough review of the existing online reputation systems and their challenges in use, this paper studied a case of Amazon’s reputation system for the impacts of Web 2.0. Through our case study, several distinguished features of new generation reputation systems are noted including multimedia feedbacks, reviewer centered, folksonomy (use of tag), community contribution, comprehensive reputation, dynamic and interactive system etc.. These new developments promise a path that move towards a trustworthy and reliable online reputation system in the Web 2.0 era

Examining the Temperature Dependence of Louche Formation in Absinthe

Absinthe is an anise-flavored alcohol that is typically served by adding cold water to form a cloudy green louche, similar to the cloudy white louche of ouzo. This microemulsion formation, due to the competing interactions within the oil-alcohol-water system, has been termed the ouzo effect. Previous work has examined the ternary oil-alcohol-water phase diagram in ouzo and limoncello. Additional work has also characterized the droplet size and stability of microemulsions in ouzo, limoncello, and pastis. However, less work has been done to examine the effect of temperature on louche formation despite the fact that the louche is traditionally formed by adding ice cold water. This work demonstrates that both the maximum turbidity and the fraction of alcohol at maximum turbidity are temperature-dependent. The louche formation can be fit with a logistic curve, and the resulting fit parameters are linear with temperature. Optical images show that the increased turbidity correlates with an increase in the number of droplets in the microemulsion

First exit times of solutions of stochastic differential equations driven by multiplicative Levy noise with heavy tails

In this paper we study first exit times from a bounded domain of a gradient dynamical system $\dot Y_t=-\nabla U(Y_t)$ perturbed by a small multiplicative L\'evy noise with heavy tails. A special attention is paid to the way the multiplicative noise is introduced. In particular we determine the asymptotics of the first exit time of solutions of It\^o, Stratonovich and Marcus canonical SDEs.Comment: 19 pages, 2 figure

Estimation of conditional laws given an extreme component

Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t)$ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector $(X,Y)$, suitably normalized, given that $X$ is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist) and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated through simulations.Comment: 32 pages, 5 figur

Early affective changes and increased connectivity in preclinical Alzheimer's disease.

IntroductionAffective changes precede cognitive decline in mild Alzheimer's disease and may relate to increased connectivity in a "salience network" attuned to emotionally significant stimuli. The trajectory of affective changes in preclinical Alzheimer's disease, and its relationship to this network, is unknown.MethodsOne hundred one cognitively normal older adults received longitudinal assessments of affective symptoms, then amyloid-PET. We hypothesized amyloid-positive individuals would show enhanced emotional reactivity associated with salience network connectivity. We tested whether increased global connectivity in key regions significantly related to affective changes.ResultsIn participants later found to be amyloid positive, emotional reactivity increased with age, and interpersonal warmth declined in women. These individuals showed higher global connectivity within the right insula and superior temporal sulcus; higher superior temporal sulcus connectivity predicted increasing emotional reactivity and decreasing interpersonal warmth.ConclusionsAffective changes should be considered an early preclinical feature of Alzheimer's disease. These changes may relate to higher functional connectivity in regions critical for social-emotional processing