Dependence structures of multivariate Bernoulli random vectors

AbstractIn some situations, it is difficult and tedious to check notions of dependence properties and dependence orders for multivariate distributions supported on a finite lattice. The purpose of this paper is to utilize a newly developed tool, majorization with respect to weighted trees, to lay out some general results that can be used to identify some dependence properties and dependence orders for multivariate Bernoulli random vectors. Such a study gives us some new insight into the relations between the concepts of dependence

Dimension reduction and parameter estimation for additive index models *

In this paper, we consider simultaneous model selection and estimation for the additive index model. The additive index model is a class of structured nonparametric models that can be expressed as additive models of a set of unknown linear transformation of the original predictor variables. We introduce a penalized least squares estimator and discuss how it can be efficiently computed in practice. Both theoretical and empirical properties of the estimate are presented to demonstrate its merits. Extensions to more general prediction framework are also discussed

The role of patient volunteers in Fangcang Shelter Hospital during the Omicron wave of COVID-19 pandemic in Shanghai, China: a qualitative study

ObjectiveDuring the Omicron wave of the COVID-19 pandemic in Shanghai, Fangcang Shelter Hospital (FSH) served as the major way in patient quarantine. Many COVID patients served as volunteers in FSH providing a lot of assistance for the medical workers and other COVID patients. The aim of this study was to explore the experiences of patient volunteers in FSH. It helps health professionals better understand their motivational incentives and barriers in their volunteer work, and improves recruiting and managing volunteers in subsequent public health emergencies.MethodsThis is a qualitative study using semi-structured interviews. Thirteen patient volunteers working in an FSH in Shanghai were included. Thematic analysis was applied to data analysis.ResultsFour themes and nine subthemes were identified. The wishes to give back to society and the responsibility of politics and religion were the main reasons for the patients to serve as volunteers in FSH. The patient volunteers served as the bridge to reduce the communication barriers between other patients and healthcare professionals. They also provided support in supply distribution and psychological counseling. They viewed voluntary work as a usual task and tried to solve the barriers in their work. In turn, the voluntary work brought them benefits in mental and physical health, as well as another chance for growth.ConclusionWorking as volunteers in FSHs not only brought personal benefits to the COVID patients but also fulfilled the needs of the healthcare system during public health emergencies. The mode of mutual help between patients could be taken as an example in other public health emergencies

Statistical analysis of high dimensional data

This century is surely the century of data (Donoho, 2000). Data analysis has been an emerging activity over the last few decades. High dimensional data is in particular more and more pervasive with the advance of massive data collection system, such as microarrays, satellite imagery, and financial data. However, analysis of high dimensional data is of challenge with the so called curse of dimensionality (Bellman 1961). This research dissertation presents several methodologies in the application of high dimensional data analysis. The first part discusses a joint analysis of multiple microarray gene expressions. Microarray analysis dates back to Golub et al. (1999). It draws much attention after that. One common goal of microarray analysis is to determine which genes are differentially expressed. These genes behave significantly differently between groups of individuals. However, in microarray analysis, there are thousands of genes but few arrays (samples, individuals) and thus relatively low reproducibility remains. It is natural to consider joint analyses that could combine microarrays from different experiments effectively in order to achieve improved accuracy. In particular, we present a model-based approach for better identification of differentially expressed genes by incorporating data from different studies. The model can accommodate in a seamless fashion a wide range of studies including those performed at different platforms, and/or under different but overlapping biological conditions. Model-based inferences can be done in an empirical Bayes fashion. Because of the information sharing among studies, the joint analysis dramatically improves inferences based on individual analysis. Simulation studies and real data examples are presented to demonstrate the effectiveness of the proposed approach under a variety of complications that often arise in practice. The second part is about covariance matrix estimation in high dimensional data. First, we propose a penalised likelihood estimator for high dimensional t-distribution. The student t-distribution is of increasing interest in mathematical finance, education and many other applications. However, the application in t-distribution is limited by the difficulty in the parameter estimation of the covariance matrix for high dimensional data. We show that by imposing LASSO penalty on the Cholesky factors of the covariance matrix, EM algorithm can efficiently compute the estimator and it performs much better than other popular estimators. Secondly, we propose an estimator for high dimensional Gaussian mixture models. Finite Gaussian mixture models are widely used in statistics thanks to its great flexibility. However, parameter estimation for Gaussian mixture models with high dimensionality can be rather challenging because of the huge number of parameters that need to be estimated. For such purposes, we propose a penalized likelihood estimator to specifically address such difficulties. The LASSO penalty we impose on the inverse covariance matrices encourages sparsity on its entries and therefore helps reducing the dimensionality of the problem. We show that the proposed estimator can be efficiently computed via an Expectation-Maximization algorithm. To illustrate the practical merits of the proposed method, we consider its application in model-based clustering and mixture discriminant analysis. Numerical experiments with both simulated and real data show that the new method is a valuable tool in handling high dimensional data. Finally, we present structured estimators for high dimensional Gaussian mixture models. The graphical representation of every cluster in Gaussian mixture models may have the same or similar structure, which is an important feature in many applications, such as image processing, speech recognition and gene network analysis. Failure to consider the sharing structure would deteriorate the estimation accuracy. To address such issues, we propose two structured estimators, hierarchical Lasso estimator and group Lasso estimator. An EM algorithm can be applied to conveniently solve the estimation problem. We show that when clusters share similar structures, the proposed estimator perform much better than the separate Lasso estimator.Ph.D.Committee Chair: Ming Yuan; Committee Member: JC Lu; Committee Member: Nicoleta Serban; Committee Member: Xiaoming Huo; Committee Member: Yixin Fan

Dependence structures of multivariate Bernoulli random vectors

In some situations, it is difficult and tedious to check notions of dependence properties and dependence orders for multivariate distributions supported on a finite lattice. The purpose of this paper is to utilize a newly developed tool, majorization with respect to weighted trees, to lay out some general results that can be used to identify some dependence properties and dependence orders for multivariate Bernoulli random vectors. Such a study gives us some new insight into the relations between the concepts of dependence.Weakly positive (negatively) associated Positively (negatively) supermodular dependent Strongly positive (negative) orthant dependent Positive (negative) orthant dependent Supermodular order Concordance order Majorization with respect to weighted trees Probability trees

Molecular Mechanism of Specific Recognition of Cubic Pt Nanocrystals by Peptides and of the Concentration-Dependent Formation from Seed Crystals

Metal nanocrystals enable new functionality in sensors, biomarkers, and catalysts while mechanisms of shape-control in synthesis remain incompletely understood. This study explains mechanisms of biomolecule recognition and ligand-directed growth of cubic platinum nanocrystals in atomic detail using molecular dynamics simulation (MD), synthesis, and characterization. Peptide T7 is shown to selectively recognize {100} bounded nanocubes through preferential adsorption near the edges as opposed to facet centers. Spatial preferences in peptide binding are related to differences in the binding of water molecules and conformational matching of polarizable atoms in the peptide to {100} epitaxial sites. Changes in peptide concentration also have profound impact on attraction versus repulsion on a given surface. As an example, the selective synthesis of cubes in the presence of peptide T7 demonstrates that only intermediate T7 concentration leads to high yield. High-resolution transmission electron microscopy (HRTEM) shows concentration-dependent changes in crystal shape, yield, and size. Large-scale MD simulations explain associated differences in facet coverage and in adsorption energies of T7 peptides on cuboctahedral seed crystals, supporting a growth mechanism of adatom deposition. A similar analysis using a different peptide S7 is presented as well. Emerging computational opportunities to predict ligand binding to metal nanocrystals and rationalize growth preferences are summarized

Data_Sheet_1_The role of patient volunteers in Fangcang Shelter Hospital during the Omicron wave of COVID-19 pandemic in Shanghai, China: a qualitative study.DOCX

ObjectiveDuring the Omicron wave of the COVID-19 pandemic in Shanghai, Fangcang Shelter Hospital (FSH) served as the major way in patient quarantine. Many COVID patients served as volunteers in FSH providing a lot of assistance for the medical workers and other COVID patients. The aim of this study was to explore the experiences of patient volunteers in FSH. It helps health professionals better understand their motivational incentives and barriers in their volunteer work, and improves recruiting and managing volunteers in subsequent public health emergencies.MethodsThis is a qualitative study using semi-structured interviews. Thirteen patient volunteers working in an FSH in Shanghai were included. Thematic analysis was applied to data analysis.ResultsFour themes and nine subthemes were identified. The wishes to give back to society and the responsibility of politics and religion were the main reasons for the patients to serve as volunteers in FSH. The patient volunteers served as the bridge to reduce the communication barriers between other patients and healthcare professionals. They also provided support in supply distribution and psychological counseling. They viewed voluntary work as a usual task and tried to solve the barriers in their work. In turn, the voluntary work brought them benefits in mental and physical health, as well as another chance for growth.ConclusionWorking as volunteers in FSHs not only brought personal benefits to the COVID patients but also fulfilled the needs of the healthcare system during public health emergencies. The mode of mutual help between patients could be taken as an example in other public health emergencies.</p