Measure Of Statistical Dependence Research Articles

A comprehensive review on the development of copulas in financial field

The Copula concept has long been used in many applications, especially in the financial field. This concept was first used in 1959 by Sklar in his mathematical work and greatly assisted in the applications of financial and insurance areas. The copula functions have been widely used in dependence modeling. In this study, we look at how the copula began to develop from a basic form to a more advanced form through studies that previous researchers have made. Throughout this study, we find various types of the copula, and each exhibits its own characteristics lying under two main families, Elliptical and Archimedean copulas. Our findings suggest that copula is vital in solving problems in statistical dependence measures and joint marginal distribution functions. This comprehensive study served as a review paper on the development of copulas from their initial existence to their latest evolution.

SUSTAINABLE DEVELOPMENT OF SMALL AND MEDIUM ENTERPRISES IN POLAND IMPLEMENTATION IN THE MULTI-DIMENSIONAL APPROACH

The implementation of the principles of sustainable development is widely recognized as one of the key elements of success and competitive advantage of modern enterprises. It is recognized that sustainable development should be incorporated into the organizations value system and function at the strategic level. Meanwhile, the range of sustainable practices and approaches used varies from enterprise to enterprise, which is determined by many variables, including enterprise size. The main purpose of the article is to assess the level of implementation of the principles of sustainable development in small and medium-sized enterprises, taking into account its economic, environmental and social elements, and to diagnose the relationship between the level of sustainability of the organization and its growth potential. To achieve the main goal and verify research hypotheses, the questionnaire survey was conducted in 2023 on a group of 100 small and medium-sized enterprises in the lskie Voivodeship. Statistical analysis was developed using descriptive statistics and Kendalls tau correlation coefficient as one of the nonparametric measures of monotonic statistical dependence. The research confirmed the existence of statistically significant, positive relationships between the economic, environmental and social dimensions of sustainable development and the growth potential of the organization.

Using kernel-based statistical distance to study the dynamics of charged particle beams in particle-based simulation codes.

Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as numerical diagnostics for simulations involving charged-particle beams. Related measures of statistical dependence are also described. The resulting diagnostics provide sensitive measures of dynamical processes important for beams in nonlinear or high-intensity systems, which are otherwise difficult to characterize. The focus is on kernel-based methods such as maximum mean discrepancy, which have a well-developed mathematical foundation and reasonable computational complexity. Several benchmark problems and examples involving intense beams are discussed. While the focus is on charged-particle beams, these methods may also be applied to other many-body systems such as plasmas or gravitational systems.

Comparison between Information Theoretic Measures to Assess Financial Markets

Information theoretic measures were applied to the study of the randomness associations of different financial time series. We studied the level of similarities between information theoretic measures and the various tools of regression analysis, i.e., between Shannon entropy and the total sum of squares of the dependent variable, relative mutual information and coefficients of correlation, conditional entropy and residual sum of squares, etc. We observed that mutual information and its dynamical extensions provide an alternative approach with some advantages to study the association between several international stock indices. Furthermore, mutual information and conditional entropy are relatively efficient compared to the measures of statistical dependence.

Statistical Dependence: Beyond Pearson’s ρ

Pearson’s ρ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known; however, that it has a number of shortcomings; in particular, for heavy tailed distributions and in nonlinear situations, where it may produce misleading, and even disastrous results. In recent years, a number of alternatives have been proposed. In this paper, we will survey these developments, especially results obtained in the last couple of decades. Among measures discussed are the copula, distribution-based measures, the distance covariance, the HSIC measure popular in machine learning and finally the local Gaussian correlation, which is a local version of Pearson’s ρ. Throughout, we put the emphasis on conceptual developments and a comparison of these. We point out relevant references to technical details as well as comparative empirical and simulated experiments. There is a broad selection of references under each topic treated.

Inferring network properties from time series using transfer entropy and mutual information: Validation of multivariate versus bivariate approaches

Functional and effective networks inferred from time series are at the core of network neuroscience. Interpreting properties of these networks requires inferred network models to reflect key underlying structural features. However, even a few spurious links can severely distort network measures, posing a challenge for functional connectomes. We study the extent to which micro- and macroscopic properties of underlying networks can be inferred by algorithms based on mutual information and bivariate/multivariate transfer entropy. The validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular). Simulations are based on a neural mass model and on autoregressive dynamics (employing Gaussian estimators for direct comparison to functional connectivity and Granger causality). We find that multivariate transfer entropy captures key properties of all network structures for longer time series. Bivariate methods can achieve higher recall (sensitivity) for shorter time series but are unable to control false positives (lower specificity) as available data increases. This leads to overestimated clustering, small-world, and rich-club coefficients, underestimated shortest path lengths and hub centrality, and fattened degree distribution tails. Caution should therefore be used when interpreting network properties of functional connectomes obtained via correlation or pairwise statistical dependence measures, rather than more holistic (yet data-hungry) multivariate models.

Probabilistic sensitivity measures as information value

Decision makers increasingly rely on forecasts or predictions generated by quantitative models. Best practices recommend that a forecast report be accompanied by a sensitivity analysis. A wide variety of probabilistic sensitivity measures have been suggested; however, model inputs may be ranked differently by different sensitivity measures. Is there some way to reduce this disparity by identifying what probabilistic sensitivity measures are most appropriate for a given reporting context? We address this question by postulating that importance rankings of model inputs generated by a sensitivity measure should correspond to the information value for those inputs in the problem of constructing an optimal report based on some proper scoring rule. While some sensitivity measures have already been identified as information value under proper scoring rules, we identify others and provide some generalizations. We address the general question of when a sensitivity measure has this property, presenting necessary and sufficient conditions. We directly examine whether sensitivity measures retain important properties such as transformation invariance and compliance with Renyi’s Postulate D for measures of statistical dependence. These results provide a means for selecting the most appropriate sensitivity measures for a particular reporting context and provide the analyst reasonable justifications for that selection. We illustrate these ideas using a large scale probabilistic safety assessment case study used to support decision making in the design and planning of a lunar space mission.

Nowa miara zależności statystycznej wyborów od grupy

Artykuł przedstawia propozycję nowego typu zależności statystycznej. Niezależność statystyczna tego rodzaju oznacza identyczność uporządkowania częstości wyborów kategorii we wszystkich grupach. Zgodność między wyborami będzie oceniana za pomocą miary różnorodności. Określona będzie nowa miara zależności statystycznej, jej własności i interpretacja.

Stationary distribution of the linkage disequilibrium coefficient [formula omitted

The linkage disequilibrium coefficient r2 is a measure of statistical dependence of the alleles possessed by an individual at different genetic loci. It is widely used in association studies to search for the locations of disease-causing genes on chromosomes. Most studies to date treat r2 as a fixed property of two loci in a finite population, and investigate the sampling distribution of estimators due to the statistical sampling of individuals from the population. Here, we instead consider the distribution of r2 itself under a process of genetic sampling through the generations. Using a classical two-locus model for genetic drift, mutation, and recombination, we investigate the probability density function of r2 at stationarity. This density function provides a tool for inference on evolutionary parameters such as mutation and recombination rates. We reconstruct the approximate stationary density of r2 by calculating a finite sequence of the distribution’s moments and applying the maximum entropy principle. Our approach is based on the diffusion approximation, under which we demonstrate that for certain models in population genetics, moments of the stationary distribution can be obtained without knowing the probability distribution itself. To illustrate our approach, we show how the stationary probability density of r2 can be used in a maximum likelihood framework to estimate mutation and recombination rates from sample data of r2.

Medium-low resolution multisource remote sensing image registration based on SIFT and robust regional mutual information

ABSTRACTOwing to significant geometric distortions and illumination differences, high precision and robust matching of multisource remote sensing images is a difficult task. To solve this, mutual information (MI)-based methods have been a preferred choice, as MI represents a measure of statistical dependence between the two images. However, MI only considers original grey information and neglects spatial information in the calculation of the probability distribution. In this paper, a novel similarity metric based on rotationally invariant regional mutual information (RIRMI) is proposed. The RIRMI metric is constructed by combining MI with a regional information based on the statistical relationship between rotationally invariant centre-symmetric local binary patterns of the images. The similarity metric based on RIRMI considers not only the spatial information, but the effect of the local grey variations and rotation changes on computing probability density function as well. The proposed method is tested on various simulated remote sensing images (5–30 m GSD) and real remote sensing images (2–30 m GSD) which are taken at different sensors, spectral bands, and times. Results verify that RIRMI is more robust and accurate than the common MI-based registration method.

A Bayesian Nonparametric Approach to Testing for Dependence Between Random Variables

Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity assumptions implicit in traditional association scores such as correlation. Here we describe a Bayesian nonparametric procedure that leads to a tractable, explicit and analytic quantification of the relative evidence for dependence vs independence. Our approach uses Polya tree priors on the space of probability measures which can then be embedded within a decision theoretic test for dependence. Polya tree priors can accommodate known uncertainty in the form of the underlying sampling distribution and provides an explicit posterior probability measure of both dependence and independence. Well known advantages of having an explicit probability measure include: easy comparison of evidence across different studies; encoding prior information; quantifying changes in dependence across different experimental conditions, and the integration of results within formal decision analysis.

Transition to reconstructibility in weakly coupled networks.

Across scientific disciplines, thresholded pairwise measures of statistical dependence between time series are taken as proxies for the interactions between the dynamical units of a network. Yet such correlation measures often fail to reflect the underlying physical interactions accurately. Here we systematically study the problem of reconstructing direct physical interaction networks from thresholding correlations. We explicate how local common cause and relay structures, heterogeneous in-degrees and non-local structural properties of the network generally hinder reconstructibility. However, in the limit of weak coupling strengths we prove that stationary systems with dynamics close to a given operating point transition to universal reconstructiblity across all network topologies.

On mutual information for elliptical distributions: a case of nonlinear dependence of ‘n’ vectors

In this paper, we modeled dependent categorical data via mutual information concept to obtain the measure of statistical dependence. We first derive the entropy and mutual information index for exponential power distribution. These concepts are important and were developed by Shannon in the context of information theory. Several literatures are already published in the case of the multivariate normal distribution. Then we extend these tools to the special case of a full symmetric of multivariate elliptical distributions. The upper bound for the entropy which is attained for the normal density is established. We further derived the nonlinear joint model for dependent random vectors that spans an elliptical vector space to enhance multivariate relationships among non-empty subsets of vectors via multivariate mutual information; based on the assumption that the subsets of each vector and their interactions can be represented in discrete form. To illustrate its application, the multivariate dependency among various sites based on dominance of some attributes were investigated.

Direct Estimation of the Derivative of Quadratic Mutual Information with Application in Supervised Dimension Reduction.

A typical goal of linear-supervised dimension reduction is to find a low-dimensional subspace of the input space such that the projected input variables preserve maximal information about the output variables. The dependence-maximization approach solves the supervised dimension-reduction problem through maximizing a statistical dependence between projected input variables and output variables. A well-known statistical dependence measure is mutual information (MI), which is based on the Kullback-Leibler (KL) divergence. However, it is known that the KL divergence is sensitive to outliers. Quadratic MI (QMI) is a variant of MI based on the [Formula: see text] distance, which is more robust against outliers than the KL divergence, and a computationally efficient method to estimate QMI from data, least squares QMI (LSQMI), has been proposed recently. For these reasons, developing a supervised dimension-reduction method based on LSQMI seems promising. However, not QMI itself but the derivative of QMI is needed for subspace search in linear-supervised dimension reduction, and the derivative of an accurate QMI estimator is not necessarily a good estimator of the derivative of QMI. In this letter, we propose to directly estimate the derivative of QMI without estimating QMI itself. We show that the direct estimation of the derivative of QMI is more accurate than the derivative of the estimated QMI. Finally, we develop a linear-supervised dimension-reduction algorithm that efficiently uses the proposed derivative estimator and demonstrate through experiments that the proposed method is more robust against outliers than existing methods.

Kernel learning and optimization with Hilbert–Schmidt independence criterion

Measures of statistical dependence between random variables have been successfully applied in many machine learning tasks, such as independent component analysis, feature selection, clustering and dimensionality reduction. The success is based on the fact that many existing learning tasks can be cast into problems of dependence maximization (or minimization). Motivated by this, we present a unifying view of kernel learning via statistical dependence estimation. The key idea is that good kernels should maximize the statistical dependence between the kernels and the class labels. The dependence is measured by the Hilbert–Schmidt independence criterion (HSIC), which is based on computing the Hilbert–Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces and is traditionally used to measure the statistical dependence between random variables. As a special case of kernel learning, we propose a Gaussian kernel optimization method for classification by maximizing the HSIC, where two forms of Gaussian kernels (spherical kernel and ellipsoidal kernel) are considered. Extensive experiments on real-world data sets from UCI benchmark repository validate the superiority of the proposed approach in terms of both prediction accuracy and computational efficiency.

Blood pressure and pulse interval coupling: A copula approach.

In this paper a copula approach is applied as a tool for assessing the measure of statistical dependence of parallel cardiovascular time series. Families of Archimedean copulas (Clayton, Frank and Gumbel) are applied to pulse interval, systolic and diastolic blood pressure recorded from male Wistar rats at baseline conditions, and to their isodistributional surrogates with the same marginal, but randomized joint distribution functions. The influence of time offset of the parallel time series is explored. The amount of data required for a stable working point is discussed.

Quantum-classical transition and quantum activation of ratchet currents in the parameter space.

The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero-temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed based on quantum, semiclassical, and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.

Independently controlled wing stroke patterns in the fruit fly Drosophila melanogaster.

Flies achieve supreme flight maneuverability through a small set of miniscule steering muscles attached to the wing base. The fast flight maneuvers arise from precisely timed activation of the steering muscles and the resulting subtle modulation of the wing stroke. In addition, slower modulation of wing kinematics arises from changes in the activity of indirect flight muscles in the thorax. We investigated if these modulations can be described as a superposition of a limited number of elementary deformations of the wing stroke that are under independent physiological control. Using a high-speed computer vision system, we recorded the wing motion of tethered flying fruit flies for up to 12 000 consecutive wing strokes at a sampling rate of 6250 Hz. We then decomposed the joint motion pattern of both wings into components that had the minimal mutual information (a measure of statistical dependence). In 100 flight segments measured from 10 individual flies, we identified 7 distinct types of frequently occurring least-dependent components, each defining a kinematic pattern (a specific deformation of the wing stroke and the sequence of its activation from cycle to cycle). Two of these stroke deformations can be associated with the control of yaw torque and total flight force, respectively. A third deformation involves a change in the downstroke-to-upstroke duration ratio, which is expected to alter the pitch torque. A fourth kinematic pattern consists in the alteration of stroke amplitude with a period of 2 wingbeat cycles, extending for dozens of cycles. Our analysis indicates that these four elementary kinematic patterns can be activated mutually independently, and occur both in isolation and in linear superposition. The results strengthen the available evidence for independent control of yaw torque, pitch torque, and total flight force. Our computational method facilitates systematic identification of novel patterns in large kinematic datasets.

Deformable multi-modal image registration by maximizing Rényi's statistical dependence measure

A novel variational model for deformable multi-modal image registration is presented in this work. As an alternative to the models based on maximizing mutual information, the Rényi's statistical dependence measure of two random variables is proposed as a measure of the goodness of matching in our objective functional. The proposed model does not require an estimation of the continuous joint probability density function. Instead, it only needs observed independent instances. Moreover, the theory of reproducing kernel Hilbert space is used to simplify the computation. Experimental results and comparisons with several existing methods are provided to show the effectiveness of the model.

Dependence clustering, a method revealing community structure with group dependence

We propose a clustering method maximizing a new measure called “group dependence.” Group dependence quantifies how precise a certain division of a graph is in terms of dependence distance. Built upon statistical dependence measure between points driven by Markovian transitions, group dependence incorporates the geometric structure of input data. Besides capturing degrees of positive dependence and coherence for a group division, group dependence inherently supplies the proposed clustering method with a definite decision on the depth of division. We provide an optimality aspect of the method as theoretical justification in consideration of posterior transition probabilities of input data. Illustrating its procedure using data from a known structure, we demonstrate its performance in the clustering task of real-world data sets, Amazon, DBLP, and YouTube, in comparison with selected clustering algorithms. We show that the proposed method outperforms the selected methods in reasonable settings: in particular, the proposed method surpasses modularity clustering in terms of normalized mutual information. We also show that the proposed method reveals additional insights on community structure detection according to its connectivity scale parameter.