Graphical Methods Of Data Analysis Research Articles

Sampling constrained continuous probability distributions: A review

AbstractThe problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Markov Chain Monte Carlo (MCMC) sampling methods have been adapted to handle different types of constraints on random variables. Among these methods, Hamilton Monte Carlo (HMC) and the related approaches have shown significant advantages in terms of computational efficiency compared with other counterparts. In this article, we first review HMC and some extended sampling methods, and then we concretely explain three constrained HMC‐based sampling methods, reflection, reformulation, and spherical HMC. For illustration, we apply these methods to solve three well‐known constrained sampling problems, truncated multivariate normal distributions, Bayesian regularized regression, and nonparametric density estimation. In this review, we also connect constrained sampling with another similar problem in the statistical design of experiments with constrained design space.This article is categorized under: Applications of Computational Statistics > Computational Mathematics Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical and Graphical Methods of Data Analysis > Sampling

A survey of smoothing techniques based on a backfitting algorithm in estimation of semiparametric additive models

AbstractThis paper aims to present an overview of Semiparametric additive models. An estimation of the finite‐parameters of semiparametric regression models that involve additive nonparametric components is explained, including their historical background. In addition, three different smoothing techniques are considered in order to show the working procedures of the estimators and to explore their statistical properties: smoothing splines, kernel smoothing and local linear regression. These methods are compared with respect to both their theoretical and practical behaviors. A simulation study and a real data example are carried out to reveal the performances of the three methods. Accordingly, the advantages and disadvantages of each method regarding semiparametric additive models are presented based on their comparative scores using determined evaluation metrics for loss of information.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical Models > Semiparametric Models

Diseases maps of spatial epidemiological data by R

AbstractDisease maps are essential when analyzing spatial epidemiological data, such as newly detected COVID‐19 positive cases or suicide deaths, because it is necessary to determine the method of analysis in order to perform spatial statistical analysis. Disease maps give an initial overview of the data and provide evidence of regional trends, which the analyst can check. Therefore, in this article, the author aimed to use R, a statistical data analysis tool, to draw spatial epidemiological data in the form of disease maps. This article presents three different methods and analyzes recent trends in COVID‐19 and suicide mortality. The author used monthly data from April, July, and October 2020. The results showed no significant trend in April, but some prefectures showed a negative correlation in July. On the other hand, some prefectures showed a positive correlation in October, confirming the influence of COVID‐19 on suicide by region.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

On unbiasedness and biasedness of the Wilcoxon and some nonparametric tests

AbstractIn several fields of applications, the underlying theoretical distribution is unknown and cannot be assumed to have a specific parametric distribution such as a normal distribution. Nonparametric statistical methods are preferable in these cases. Nonparametric testing hypotheses have been one of the primarily used statistical procedures for nearly a century, and the power of the test is an important property in nonparametric testing procedures. This review discusses the unbiasedness of nonparametric tests. In nonparametric hypothesis, the best‐known Wilcoxon–Mann–Whitney (WMW) test has both robustness and power performance. Therefore, the WMW test is widely used to determine the location parameter. In this review, the unbiasedness and biasedness of the WMW test for the location parameter family of the distribution is mainly investigated. An overview of historical developments, detailed discussions, and works on the unbiasedness/biasedness of several nonparametric tests are presented with references to numerous studies. Finally, we conclude this review with a discussion on the unbiasedness/biasedness of nonparametric test procedures. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

Sequential Monte Carlo optimization and statistical inference

AbstractSequential Monte Carlo (SMC) is a powerful technique originally developed for particle filtering and Bayesian inference. As a generic optimizer for statistical and nonstatistical objectives, its role is far less known. Density‐tempered SMC is a highly efficient sampling technique ideally suited for challenging global optimization problems and is implementable with a somewhat arbitrary initialization sampler instead of relying on a prior distribution. SMC optimization is anchored at the fact that all optimization tasks (continuous, discontinuous, combinatorial, or noisy objective function) can be turned into sampling under a density or probability function short of a norming constant. The point with the highest functional value is the SMC estimate for the maximum. Through examples, we systematically present various density‐tempered SMC algorithms and their superior performance vs. other techniques like Markov Chain Monte Carlo. Data cloning and k‐fold duplication are two easily implementable accuracy accelerators, and their complementarity is discussed. The Extreme Value Theorem on the maximum order statistic can also help assess the quality of the SMC optimum. Our coverage includes the algorithmic essence of the density‐tempered SMC with various enhancements and solutions for (1) a bi‐modal nonstatistical function without and with constraints, (2) a multidimensional step function, (3) offline and online optimizations, (4) combinatorial variable selection, and (5) noninvertibility of the Hessian.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods Algorithms and Computational Methods > Stochastic Optimization Algorithms and Computational Methods > Integer Programming

Robust regression using probabilistically linked data

AbstractThere is growing interest in a data integration approach to survey sampling, particularly where population registers are linked for sampling and subsequent analysis. The reason for doing this is simple: it is only by linking the same individuals in the different sources that it becomes possible to create a data set suitable for analysis. But data linkage is not error free. Many linkages are nondeterministic, based on how likely a linking decision corresponds to a correct match, that is, it brings together the same individual in all sources. High quality linking will ensure that the probability of this happening is high. Analysis of the linked data should take account of this additional source of error when this is not the case. This is especially true for secondary analysis carried out without access to the linking information, that is, the often confidential data that agencies use in their record matching. We describe an inferential framework that allows for linkage errors when sampling from linked registers. After first reviewing current research activity in this area, we focus on secondary analysis and linear regression modeling, including the important special case of estimation of subpopulation and small area means. In doing so we consider both robustness and efficiency of the resulting linked data inferences.This article is categorized under: Algorithms and Computational Methods > Maximum Likelihood Methods Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

Projection‐based techniques for high‐dimensional optimal transport problems

AbstractOptimal transport (OT) methods seek a transformation map (or plan) between two probability measures, such that the transformation has the minimum transportation cost. Such a minimum transport cost, with a certain power transform, is called the Wasserstein distance. Recently, OT methods have drawn great attention in statistics, machine learning, and computer science, especially in deep generative neural networks. Despite its broad applications, the estimation of high‐dimensional Wasserstein distances is a well‐known challenging problem owing to the curse‐of‐dimensionality. There are some cutting‐edge projection‐based techniques that tackle high‐dimensional OT problems. Three major approaches of such techniques are introduced, respectively, the slicing approach, the iterative projection approach, and the projection robust OT approach. Open challenges are discussed at the end of the review.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning

The how and why of Bayesian nonparametric causal inference

AbstractSpurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high‐dimensional) methods have recently seen increased attention in the causal inference literature. In this article, we present a comprehensive overview of Bayesian nonparametric applications to causal inference. Our aims are to (i) introduce the fundamental Bayesian nonparametric toolkit; (ii) discuss how to determine which tool is most appropriate for a given problem; and (iii) show how to avoid common pitfalls in applying Bayesian nonparametric methods in high‐dimensional settings. Unlike standard fixed‐dimensional parametric problems, where outcome modeling alone can sometimes be effective, we argue that most of the time it is necessary to model both the selection and outcome processes.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

The state‐of‐the‐art on tours for dynamic visualization of high‐dimensional data

AbstractThis article discusses a high‐dimensional visualization technique called the tour, which can be used to view data in more than three dimensions. We review the theory and history behind the technique, as well as modern software developments and applications of the tour that are being found across the sciences and machine learning.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis

Ordered and censored lifetime data in reliability: An illustrative review

AbstractThe present review provides a survey on basic models of ordered data and censoring mechanisms with a focus on lifetime data, failure data, and reliability applications. Throughout, illustrations of the data generation process as well as of the censoring mechanisms are used to visualize these procedures. By example we present basic results assuming a life testing model with independent and identically distributed measurements and focus on selected inferential results for exponentially distributed lifetimes. In particular, we aim to illustrate similarities between the models as well as to highlight some interesting exact statistical results. It is not intended to survey all possible model assumptions, probabilistic results, and used inferential methods used in this framework. For this purpose as well as for further reading, we provide an extensive bibliography.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Reliability, Survivability, and Quality Control Algorithms and Computational Methods > Maximum Likelihood Methods Data: Types and Structure > Traditional Statistical Data

Regression with linked datasets subject to linkage error

AbstractData are often collected from multiple heterogeneous sources and are combined subsequently. In combing data, record linkage is an essential task for linking records in datasets that refer to the same entity. Record linkage is generally not error‐free; there is a possibility that records belonging to different entities are linked or that records belonging to the same entity are missed. It is not advisable to simply ignore such errors because they can lead to data contamination and introduce bias in sample selection or estimation, which, in return, can lead to misleading statistical results and conclusions. For a long while, this problem was not properly recognized, but in recent years a growing number of researchers have developed methodology for dealing with linkage errors in regression analysis with linked datasets. The main goal of this overview is to give an account of those developments, with an emphasis on recent approaches and their connection to the so‐called “Broken Sample” problem. We also provide a short empirical study that illustrates the efficacy of corrective methods in different scenarios.This article is categorized under:Statistical Models > Model SelectionStatistical and Graphical Methods of Data Analysis > Robust MethodsStatistical and Graphical Methods of Data Analysis > Multivariate Analysis

Computational aspects of stable distributions

AbstractStable distributions are a class of probability distributions that generalize the normal distribution. They are the only possible limits of normalized sums of independent, identically distributed terms, so sums of a large number of such terms have to approach a stable law. The non‐Gaussian stable distributions have heavy tails with infinite variance, and can be skewed. In most cases, there are no known formulas for the density or cumulative distribution function of these laws, so using them in practice requires significant computational methods. This paper explains some of the computations used to make stable laws useful in practical problems.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization Algorithms and Computational Methods > Algorithms Algorithms and Computational Methods > Maximum Likelihood Methods

Bayesian modeling of multivariate time series of counts

AbstractIn this article, we present an overview of recent advances in Bayesian modeling and analysis of multivariate time series of counts. We discuss basic modeling strategies including integer valued autoregressive processes, multivariate Poisson time series and dynamic latent factor models. In so doing, we make a connection with univariate modeling frameworks such as dynamic generalized models, Poisson state space models with gamma evolution and present Bayesian approaches that extend these frameworks to multivariate setting. During our development, recent Bayesian approaches to the analysis of integer valued autoregressive processes and multivariate Poisson models are highlighted and concepts such as “decouple/recouple” and “common random environment” are presented. The role that these concepts play in Bayesian modeling and analysis of multivariate time series are discussed. Computational issues associated with Bayesian inference and forecasting from these models are also considered.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical Models > Time Series Models

Sample and realized minimum variance portfolios: Estimation, statistical inference, and tests

AbstractThe global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean‐variance efficient frontier. The estimation of the GMVP weights is therefore of much importance for financial investors. The GMVP weights depend only on the inverse covariance matrix of returns on financial risky assets, for this reason the estimated GMVP weights are subject to substantial estimation risk, especially in high‐dimensional portfolio settings. In this paper we review the recent literature on traditional sample estimators for the unconditional GMVP weights which are typically based on daily asset returns, as well as on modern realized estimators for the conditional GMVP weights based on intraday high‐frequency returns. We present various types of GMVP estimators with the corresponding stochastic results, discuss statistical tests and point on some directions for further research. Our empirical application illustrates selected properties of realized GMVP weights.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Models > Multivariate Models

Copulae: An overview and recent developments

AbstractOver the decades that have passed since they were introduced, copulae still remain a very powerful tool for modeling and estimating multivariate distributions. This work gives an overview of copula theory and it also summarizes the latest results. This article recalls the basic definition, the most important cases of bivariate copulae, and it then proceeds to a sketch of how multivariate copulae are developed both from bivariate copulae and from scratch. Regarding higher dimensions, the focus is on hierarchical Archimedean, vine, and factor copulae, which are the most often used and most flexible ways to introduce copulae to multivariate distributions. We also provide an overview of how copulae can be used in various fields of data science, including recent results. These fields include but are not limited to time series and machine learning. Finally, we describe estimation and testing methods for copulae in general, their application to the presented copula structures, and we give some specific testing and estimation procedures for those specific copulae.This article is categorized under: Statistical Models > Multivariate Models Statistical Models > Semiparametric Models Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

Why BDeu? Regular Bayesian network structure learning with discrete and continuous variables

AbstractWe consider the problem of Bayesian network structure learning (BNSL) from data. In particular, we focus on the score‐based approach rather than the constraint‐based approach and address what score we should use for the purpose. The Bayesian Dirichlet equivalent uniform (BDeu) has been mainly used within the community of BNs (not outside of it). We know that for any model selection and any data, the fitter the data to a model, the more complex the model, and vice versa. However, recently, it was proven that BDeu violates regularity, which means that it does not balance the two factors, although it works satisfactorily (consistently) when the sample size is infinitely large. In addition, we claim that the merit of using the regular scores over the BDeu is that tighter bounds of pruning rules are available when we consider efficient BNSL. Finally, using experiments, we compare the performances of the procedures to examine the claim. (This paper is for review and gives a unified viewpoint from the recent progress on the topic.)This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

A review of second-order blind identification methods.

Second‐order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high‐dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high‐dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second‐order statistics—hence the name “second‐order source separation.” In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed.This article is categorized under:Statistical Models > Time Series ModelsStatistical and Graphical Methods of Data Analysis > Dimension ReductionData: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Improving the Gibbs sampler

AbstractThe Gibbs sampler is a simple but very powerful algorithm used to simulate from a complex high‐dimensional distribution. It is particularly useful in Bayesian analysis when a complex Bayesian model involves a number of model parameters and the conditional posterior distribution of each component given the others can be derived as a standard distribution. In the presence of a strong correlation structure among components, however, the Gibbs sampler can be criticized for its slow convergence. Here we discuss several algorithmic strategies such as blocking, collapsing, and partial collapsing that are available for improving the convergence characteristics of the Gibbs sampler.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Sampling

Sampling James R. Thompson's inspired nonparametric portfolio approaches

AbstractAsset or security returns are an example of phenomena whose distributions still cannot be convincingly modeled in a parametric framework. James R. (Jim) Thompson (1938–2017) used a variety of nonparametric approaches to develop workable investing solutions in such an environment. We review his ground breaking exploration of the veracity of the capital asset pricing model (CAPM), and several nonparametric approaches to portfolio formulation including the Simugram™, variants of his Max‐Median rule, and Tukey weightings.This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > Transformations Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms

Zero‐inflated modeling part II: Zero‐inflated models for complex data structures

AbstractThe prequel to this review provided an extensive treatment of classic zero‐inflated count regression models where a univariate discrete distribution is used for the count regression component of the model. The treatment of zero inflation beyond the classic univariate count regression setting has seen a substantial increase in recent years. This second review paper surveys some of this recent literature and focuses on important developments in handling zero inflation for correlated count settings, discrete time series models, spatial models, and multivariate models. We discuss some of the available computational tools for performing estimation in these settings, while again highlighting the diverse data problems that have been addressed using these methods.This article is categorized under: Statistical Models > Multivariate Models Statistical Models > Generalized Linear Models Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory