Tensor Decomposition With Generalized Lasso Penalties

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for PTD is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas and motion-capture data from video cameras. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multiway data that exhibit smooth spatial or temporal features.     

Sufficient Dimension Reduction and Variable Selection for Large-p-Small-n Data With Highly Correlated Predictors

Sufficient dimension reduction (SDR) is a paradigm for reducing the dimension of the predictors without losing regression information. Most SDR methods require inverting the covariance matrix of the predictors. This hinders their use in the analysis of contemporary datasets where the number of predictors exceeds the available sample size and the predictors are highly correlated. To this end, by incorporating the seeded SDR idea and the sequential dimension-reduction framework, we propose a SDR method for high-dimensional data with correlated predictors. The performance of the proposed method is studied via extensive simulations. To demonstrate its use, an application to microarray gene expression data where the response is the production rate of riboflavin (vitamin B₂) is presented.     

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

Phase II monitoring of changes in mean from high‐dimensional data

The generalized T² chart (GT‐chart), which is composed of the T² statistic based on a small number of principal components and the remaining components, is a popular alternative to the traditional Hotelling's T² control chart. However, the application of the GT‐chart to high‐dimensional data, which are now ubiquitous, encounters difficulties from high dimensionality similar to other multivariate procedures. The sample principal components and their eigenvalues do not consistently estimate the population values, and the GT‐chart relying on them is also inconsistent in estimating the control limits. In this paper, we investigate the effects of high dimensionality on the GT‐chart and then propose a corrected GT‐chart using the recent results of random matrix theory for the spiked covariance model. We numerically show that the corrected GT‐chart exhibits superior performance compared to the existing methods, including the GT‐chart and Hotelling's T² control chart, under various high‐dimensional cases. Finally, we apply the proposed corrected GT‐chart to monitor chemical processes introduced in the literature.     

Semiparametric Bayesian inference for mean-covariance regression models

In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.     

Reconstruction of the Linear Ordinary Differential System Based on Discrete Points

In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.     

SMART: A data reporting standard for mass spectrometry imaging By Ying Xi,Alexandria L. Sohn,Alena N. Joignant,Stephanie M. Cologna,Boone M. Prentice and David C. Muddiman

Mass spectrometry imaging (MSI) is an important analytical technique that simultaneously reports the spatial location and abundance of detected ions in biological, chemical, clinical, and pharmaceutical studies. As MSI grows in popularity, it has become evident that data reporting varies among different research groups and between techniques. The lack of consistency in data reporting inherently creates additional challenges in comparing intra- and inter-laboratory MSI data. In this tutorial, we propose a unified data reporting system, SMART, based on the common features shared between techniques. While there are limitations to any reporting system, SMART was decided upon after significant discussion to more easily understand and benchmark MSI data. SMART is not intended to be comprehensive but rather capture essential baseline information for a given MSI study; this could be within a study (e.g., effect of spot size on the measured ion signals) or between two studies (e.g., different MSI platform technologies applied to the same tissue type). This tutorial does not attempt to address the confidence with which annotations are made nor does it deny the importance of other parameters that are not included in the current SMART format. Ultimately, the goal of this tutorial is to discuss the necessity of establishing a uniform reporting system to communicate MSI data in publications and presentations in a simple format to readily interpret the parameters and baseline outcomes of the data.     

阳离子树脂交换分离-电感耦合等离子体质谱(ICP-MS)法测定地质石膏样品中硼

硼石膏近些年在水泥、沥青混合材料等领域应用广泛,其主要成分为CaSO4·2H2O和B2O3以及其他杂质,因此准确、快速测定石膏样品中的硼元素对石膏的应用、资源综合利用等方面具有重要意义。而国家标准GB/T 5484-2012《石膏分析方法》中并没有硼元素的化学分析方法,且相关文献报道也很少。目前测定硼元素主要采用电感耦合等离子体质谱法（ICP-MS）,样品前处理多采用酸溶法,而碱熔法应用不多,主要原因是碱熔后溶液中产生大量盐分影响等离子体焰的稳定性,而732型阳离子交换树脂能吸附大量的钠离子,同时吸附了钙、镍、铁及稀土等阳离子,减少盐分干扰。基于此原理,本文采用氢氧化钠碱熔-732型阳离子交换树脂交换分离,在线加入铑内标的方式,建立了ICP-MS法测定石膏中硼的方法,同时由于石膏国家标准物质不包含硼元素的含量,采用高纯硫酸钙分别与岩石标准物质、水系沉积物国家标准物质和土壤国家标准物质混合配置成人工标准物质,并讨论了熔矿体系、阳离子加入量与吸附时间、清洗液、同位素的选择等实验条件。本方法的检出限为0.76μg/g,精密度（RSD,n=7）为0.9%~1.7%,相对误差为1.56%~3.96%,加标回收率在97.5%~102%,该方法快速、准确,记忆效应小,适合石膏中硼元素的测定。