Kernel density estimation via diffusion

We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.Comment: Published in at http://dx.doi.org/10.1214/10-AOS799 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite ``phase spaces'' can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the ``phase'' giving the state of the first queue and the ``level'' giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts's R-matrix and show that the decay rate of the stationary distribution of the ``level'' process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.Comment: Published at http://dx.doi.org/10.1214/105051604000000477 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Global Likelihood Optimization Via The Cross-Entropy Method With An Application To Mixture Models

Global likelihood maximization is an important aspect of many statistical analyses. Often the likelihood function is highly multi-extremal. This presents a significant challenge to standard search procedures, which often settle too quickly into an inferior local maximum. We present a new approach based on the cross-entropy (CE) method, and illustrate its use for the analysis of mixture models

The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method

The tree cut and merge algorithm for estimation of network reliability

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.K.P. Hui, N. Bean, M. Kraetzl and D. Kroes

On the decay rates of buffers in continuous flow lines

Consider a tandem system of machines separated by infinitely large buffers. The machines process a continuous flow of products, possibly at different speeds. The life and repair times of the machines are assumed to be exponential. We claim that the overflow probability of each buffer has an exponential decay, and provide an algorithm to determine the exact decay rates in terms of the speeds and the failure and repair rates of the machines. These decay rates provide useful qualitative insight into the behavior of the flow line. In the derivation of the algorithm we use the theory of Large Deviations

Targeting plasma cells in systemic autoimmune rheumatic diseases:Promises and pitfalls

Plasma cells are the antibody secretors of the immune system. Continuous antibody secretion over years can provide long-term immune protection but could also be held responsible for long-lasting autoimmunity in case of self-reactive plasma cells. Systemic autoimmune rheumatic diseases (ARD) affect multiple organ systems and are associated with a plethora of different autoantibodies. Two prototypic systemic ARDs are systemic lupus erythematosus (SLE) and Sjögren's disease (SjD). Both diseases are characterized by B-cell hyperactivity and the production of autoantibodies against nuclear antigens. Analogues to other immune cells, different subsets of plasma cells have been described. Plasma cell subsets are often defined dependent on their current state of maturation, that also depend on the precursor B-cell subset from which they derived. But, a universal definition of plasma cell subsets is not available so far. Furthermore, the ability for long-term survival and effector functions may differ, potentially in a disease-specific manner. Characterization of plasma cell subsets and their specificity in individual patients can help to choose a suitable targeting approach for either a broad or more selective plasma cell depletion. Targeting plasma cells in systemic ARDs is currently challenging because of side effects or varying depletion efficacies in the tissue. Recent developments, however, like antigen-specific targeting and CAR-T-cell therapy might open up major benefits for patients beyond current treatment options.</p

Heavy Tails, Importance Sampling and Cross-Entropy

We consider the problem of estimating P (Y1+ ... +Yn > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a tool for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y1+ ... +Yn > x,) n-1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some parametric examples (Pareto and Weibull) how this leads to precise answers, which as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/1 and GI/G/1 queues are also discussed

Comparing different modalities for the diagnosis of incisional hernia: a systematic review

Purpose: Incisional hernia (IH) is the most frequent complication after abdominal surgery. The diagnostic modality, observer, definition, and diagnostic protocol used for the diagnosis of IH potentially influence the reported prevalence. The objective of this systematic review is to evaluate the diagnostic accuracy of different modalities used to identify IH. Methods: Embase, MEDLINE OvidSP, Web of Science, Google Scholar, and Cochrane databases were searched to identify studies diagnosing IH. Studies comparing the IH detection rate of two different diagnostic modalities or inter-observer variability of one modality were included. Quality assessment of studies was done by Cochrane Collaboration’s tool. Article selection and data collection were performed independently by two researchers. PROSPERO registration: CRD42017062307. Results: Fifteen studies representing a total of 2986 patients were included. Inter-observer variation for CT-scan ranged from 11.2 to 69% (n = 678). Disagreement between ultrasound and CT-scan ranged between 6.6 and 17% (n = 221). Ten studies compared physical examination to CT-scan or ultrasound. Disagreement between physical examination and imaging ranged between 7.6 and 39% (n = 1602). Between 15 and 58% of IHs were solely detected by imaging (n = 483). Relative increase in IH prevalence for imaging compared to physical examination ranged from 0.92 to 2.4 (n = 1922). Conclusions: Ultrasound or CT-scan will result in substantial additional IH diagnosis. Lack of consensus regarding the definition of IH might contribute to the disagreement rates. Both the observer and diagnostic modality used could be additional factors explaining varia