Distribution-free double-sampling precedence monitoring scheme to detect unknown shifts in the location parameter

In most applications, parametric monitoring schemes are used to monitor the majority of industrial and nonindustrial processes in order to improve the quality of the outputs or services. However, parametric monitoring schemes are known to underperform when the normality assumption is not met or when there is not enough information about the symmetry or asymmetry nature of the process underlying distribution. Hence, in this paper, a new nonparametric Phase II Shewhart-type double-sampling (DS) monitoring scheme based on the precedence statistic is proposed in order to efficiently monitor quality processes when the underlying process distribution departs from normality. The performance is investigated using the average run length (ARL), standard deviation of the run length (SDRL), expected ARL (EARL) and expected average number of observations to signal (EANOS), and the average sample sizes (ASS) metrics. The latter metrics are computed using Monte Carlo simulation and exact formulae. In general, it is shown that the new DS precedence scheme outperforms the existing basic Shewhart precedence scheme with and without supplementary runs rules in many situations. A real-life illustrative example based on a filling process of milk bottles is provided to demonstrate the application and implementation of the new DS precedence monitoring scheme.     

钴系双亚胺基吡啶配合物/甲基铝氧烷体系催化乙烯齐聚

合成了 2种双亚胺基吡啶钴系催化剂 ,以甲苯为溶剂 ,甲基铝氧烷 (MAO)为助催化剂 ,用于催化乙烯齐聚合成线性α 烯烃。探讨了催化剂浓度、反应温度、n(Al) /n(Co)以及苯胺的不同对位取代基等因素对催化活性和齐聚产物分布的影响 ,找到了一些有价值的规律     

二维趋化–流体系统的整体适定性

在无通量-Dirichlet-无滑移边界条件下考虑一类趋化–流体系统的二维初边值问题。通过正则化处理和一系列的先验估计证明该系统存在整体有界的经典解。

     

Optimal Design of Blocked and Split-Plot Experiments for Fixed Effects and Variance Component Estimation

In general, modeling data from blocked and split-plot response surface experiments requires the use of generalized least squares and the estimation of two variance components. The literature on the optimal design of blocked and split-plot response surface experiments, however, focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well. To overcome this problem, we propose a new Bayesian optimal design criterion which focuses on both the variance components and the fixed effects. A novel feature of the criterion is that it incorporates prior information about the variance components through log-normal or beta prior distributions. The resulting designs allow for a more powerful statistical inference than traditional optimal designs. In our algorithm for generating optimal blocked and split-plot designs, we implement efficient quadrature approaches for the numerical approximation of the new optimal design criterion. Supplementary materials for this article are available online.     

COMMENTS ON ZELENÝ'S PAPER CONCERNING COGNITIVE EQUILIBRIA

Bivariate Pareto distributions arise naturally when it comes to comparing the performances of two systems. In this note, explicit expressions are derived for a relative measure of performance for every known bivariate Pareto distribution. The calculations involve the use of Gauss hypergeometric function.     

Hierarchical crowd analysis and anomaly detection

ObjectiveThis work proposes a novel approach to model the spatiotemporal distribution of crowd motions and detect anomalous events.MethodsWe first learn the regions of interest (ROIs) which inform the behavioral patterns by trajectory analysis with Hierarchical Dirichlet Processes (HDP), so that the main trends of crowd motions can be modeled. Based on the ROIs, we then build a series of histograms both on global and local levels as the templates for the observed movement distribution, which statistically describes time-correlated crowd events. Once the template has been built hierarchically, we import real data containing the discrete trajectory observations from video surveillance and detect abnormal events for individuals and for crowds.ResultsExperimental results show the effectiveness of our approach, which is able to analyze and extract the crowd motion information from observed trajectory dataset, and achieve the anomaly detection at the hierarchical levels.ConclusionThe proposed hierarchical approach can learn the moving trends of crowd both in global and local area and describe the crowd behaviors in statistical way, which build a template for pedestrian movement distribution that allows for the detection of time-correlated abnormal crowd events.     

Gaussian approximations in high dimensional estimation

Several estimation techniques assume validity of Gaussian approximations for estimation purposes. Interestingly, these ensemble methods have proven to work very well for high-dimensional data even when the distributions involved are not necessarily Gaussian. We attempt to bridge the gap between this oft-used computational assumption and the theoretical understanding of why this works, by employing some recent results on random projections on low dimensional subspaces and concentration inequalities.     

A sparse nonparametric hierarchical Bayesian approach towards inductive transfer for preference modeling

In this paper, we present a novel methodology for preference learning based on the concept of inductive transfer. Specifically, we introduce a nonparametric hierarchical Bayesian multitask learning approach, based on the notion that human subjects may cluster together forming groups of individuals with similar preference rationale (but not identical preferences). Our approach is facilitated by the utilization of a Dirichlet process prior, which allows for the automatic inference of the most appropriate number of subject groups (clusters), as well as the employment of the automatic relevance determination (ARD) mechanism, giving rise to a sparse nature for our model, which significantly enhances its computational efficiency. We explore the efficacy of our novel approach by applying it to both a synthetic experiment and a real-world music recommendation application. As we show, our approach offers a significant enhancement in the effectiveness of knowledge transfer in statistical preference learning applications, being capable of correctly inferring the actual number of human subject groups in a modeled dataset, and limiting knowledge transfer only to subjects belonging to the same group (wherein knowledge transferability is more likely).     

Bayesian Nonparametric Joint Mixture Model for Clustering Spatially Correlated Time Series

Abstract

We develop a Bayesian nonparametric joint mixture model for clustering spatially correlated time series based on both spatial and temporal similarities. In the temporal perspective, the pattern of a time series is flexibly modeled as a mixture of Gaussian processes, with a Dirichlet process (DP) prior over mixture components. In the spatial perspective, the spatial location is incorporated as a feature for clustering, like a time series being incorporated as a feature. Namely, we model the spatial distribution of each cluster as a DP Gaussian mixture density. For the proposed model, the number of clusters does not need to be specified in advance, but rather is automatically determined during the clustering procedure. Moreover, the spatial distribution of each cluster can be flexibly modeled with multiple modes, without determining the number of modes or specifying spatial neighborhood structures in advance. Variational inference is employed for the efficient posterior computation of the proposed model. We validate the proposed model using simulated and real-data examples. Supplementary materials for the article are available online.     

On the polynomial solvability of distributionally robust k-sum optimization

In this paper, we define a distributionally robust k-sum optimization problem as the problem of finding a solution that minimizes the worst-case expected sum of up to the k largest costs of the elements in the solution. The costs are random with a joint probability distribution that is not completely specified but rather assumed to be known to lie in a set of probability distributions. For k=1, this reduces to a distributionally robust bottleneck optimization problem while for k=n, this reduces to distributionally robust minimum sum optimization problem. Our main result is that for a Fréchet class of discrete marginal distributions with finite support, the distributionally robust k-sum combinatorial optimization problem is solvable in polynomial time if the deterministic minimum sum problem is solvable in polynomial time. This extends the result of Punnen and Aneja [On k-sum optimization, Oper. Res. Lett. 18(5)(1996), pp. 233–236] from the deterministic to the robust case. We show that this choice of the set of distributions helps preserve the submodularity of the k-sum objective function which is an useful structural property for optimization problems.