Statistical Dependence Structure Research Articles

Exploring multivariate generalized gamma manifold for color texture retrieval

This work proposes a novel method for color-textured image retrieval on a Multivariate Generalized Gamma Distribution manifold (MGΓD). Thanks to the Gaussian copula theory, we define the expression of MGΓD, which efficiently models the statistical dependence structure between dual-tree complex wavelet transform (DTCWT) of the color components. The major contribution of this paper is to provide a geometric perspective to the MGΓD by treating it as a Riemannian manifold while proposing the geodesic distance (GD) as a measure of Riemannian similarity on it. Based on information geometry tools, we conduct a geometrical study of the MGΓD manifold, allowing us to derive two suitable approximations of the GD. The experiments are performed on five well-known color texture databases, considering the content-based image retrieval (CBIR) framework and using the RGB color space. The obtained results demonstrate the efficiency of the geometric interpretation through the proposed GD as a natural and intuitive similarity measure on the studied statistical manifold.

Statistical correlation investigation of a single-doweled timber-to-timber joint

Dowel-type joints are widely used in timber structures given their ease of construction, strength, and capacity to deform before failure. The embedment strength of timber and the bending moment capacity of dowels are considered key properties in the design. On the other hand, these properties have an inherent variability that increases the uncertainties related to the connection’s strength and associated failure modes. This study proposes to quantify the uncertainty related to the statistical correlation behavior between the timber embedment strength and dowel bending moment capacity while comparing analytical solutions to the results of double shear single doweled timber joints. Traditional distribution fitting procedures, as well as copula functions, are implemented to capture their marginal and dependence behavior. Since their source of mutual correlation is known, the effectiveness of the different approaches in describing the statistical dependence structure can be assessed. This is done by investigating how equivalent are the descriptions of dependence by copula functions and directly from the correlation origin. Results obtained here indicate that, for single dowel-type connections in double shear, the impact of the copulas on the results is small, which means that improving their joint characterization represents a minor improvement in the reliability results. Besides the minor differences, the results show that copula functions are a viable tool capable of capturing the nuances of the joint behavior between random variables.

Mental State Classification Using Multi-Graph Features.

We consider the problem of extracting features from passive, multi-channel electroencephalogram (EEG) devices for downstream inference tasks related to high-level mental states such as stress and cognitive load. Our proposed feature extraction method uses recently developed spectral-based multi-graph tools and applies them to the time series of graphs implied by the statistical dependence structure (e.g., correlation) amongst the multiple sensors. We study the features in the context of two datasets each consisting of at least 30 participants and recorded using multi-channel EEG systems. We compare the classification performance of a classifier trained on the proposed features to a classifier trained on the traditional band power-based features in three settings and find that the two feature sets offer complementary predictive information. We conclude by showing that the importance of particular channels and pairs of channels for classification when using the proposed features is neuroscientifically valid.

Copula-Based Uncertainty Quantification (Copula-UQ) for Multi-Sensor Data in Structural Health Monitoring.

The problem of uncertainty quantification (UQ) for multi-sensor data is one of the main concerns in structural health monitoring (SHM). One important task is multivariate joint probability density function (PDF) modelling. Copula-based statistical inference has attracted significant attention due to the fact that it decouples inferences on the univariate marginal PDF of each random variable and the statistical dependence structure (called copula) among the random variables. This paper proposes the Copula-UQ, composing multivariate joint PDF modelling, inference on model class selection and parameter identification, and probabilistic prediction using incomplete information, for multi-sensor data measured from a SHM system. Multivariate joint PDF is modeled based on the univariate marginal PDFs and the copula. Inference is made by combing the idea of the inference functions for margins and the maximum likelihood estimate. Prediction on the PDF of the target variable, using the complete (from normal sensors) or incomplete information (due to missing data caused by sensor fault issue) of the predictor variable, are made based on the multivariate joint PDF. One example using simulated data and one example using temperature data of a multi-sensor of a monitored bridge are presented to illustrate the capability of the Copula-UQ in joint PDF modelling and target variable prediction.

False Discovery Variance Reduction in Large Scale Simultaneous Hypothesis Tests

Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the average value is acceptable (Fan et al., J Amer Statist Assoc 107(499): 1019-1035, 2012; Owen J R Stat Soc Ser B 67(3): 411–426, 2005; Qiu et al., Stat Appl Genet Mol Biol 4: 32, 2005 and Schwartzman and Lin Biometrika 98(1): 199–214, 2011). However, the statistical dependence structure of data is often unknown. Using a generic signal-processing model, Bayesian multiple testing, and simulations, we demonstrate that the variance of the false positive proportion can be substantially reduced even under unknown short range dependence. We do this by modeling the data generating process as a stationary ergodic binary signal process embedded in noisy observations. We derive conditional probabilities needed for the Bayesian multiple testing by incorporating nearby observations into a second order Taylor series approximation. Simulations under general conditions are carried out to assess the validity and the variance reduction of the approach. Along the way, we address the problem of sampling a random Markov matrix with specified stationary distribution and lower bounds on the top absolute eigenvalues, which is of interest in its own right.

Preservation of increasing convex/concave order under the formation of parallel/series system of dependent components

This paper investigates sufficient conditions for preservation property of the increasing convex order and the increasing concave order under the taking of maximum and minimum of statistically dependent random variables, respectively. As applications, we develop the preservation of NBUC and NBU(2) aging properties respectively under the parallel and series systems of components with statistically dependent lifetimes. Some copulas are presented as illustrations on statistical dependence structure satisfying the sufficient condition as well.

Concurrent credit portfolio losses.

We consider the problem of concurrent portfolio losses in two non-overlapping credit portfolios. In order to explore the full statistical dependence structure of such portfolio losses, we estimate their empirical pairwise copulas. Instead of a Gaussian dependence, we typically find a strong asymmetry in the copulas. Concurrent large portfolio losses are much more likely than small ones. Studying the dependences of these losses as a function of portfolio size, we moreover reveal that not only large portfolios of thousands of contracts, but also medium-sized and small ones with only a few dozens of contracts exhibit notable portfolio loss correlations. Anticipated idiosyncratic effects turn out to be negligible. These are troublesome insights not only for investors in structured fixed-income products, but particularly for the stability of the financial sector.JEL codes: C32, F34, G21, G32, H81.

On Bid-price Controls for Network Revenue Management

We consider a network revenue management problem and advance its dual formulation. The dual formulation reveals that the (optimal) shadow price of capacity forms a nonnegative martingale. This result is proved under minimal assumptions on network topology and stochastic nature of demand, allowing an arbitrary statistical dependence structure across time and products. Next, we consider a quadratic perturbation of the network revenue management problem and show that a simple (perturbed) bid-price control is optimal for the perturbed problem; and it is ɛ-optimal for the original network revenue management problem. Finally, we consider a predictable version of this control, where the bid prices used in the current period are last updated in the previous period, and provide an upper bound on its optimality gap in terms of the (quadratic) variation of demand. Using this upper bound we show that there exists a near-optimal such control in the usual case when periods are small compared to the planning horizon provided that either demand or the incremental information arriving during each period is small. We establish the martingale property of the (near) optimal bid prices in both settings. The martingale property can have important implications in practice as it may offer a tool for monitoring the revenue management systems.

Dynamics of major hydro-climatic variables in the headwater catchment of the Tarim River Basin, Xinjiang, China

We carried out an investigation on the effects of anthropogenic activities and climatic change on water resources in the Tarim River Basin, based on major hydro-climatic data, for the 1962–2007 period, and snow cover data from 2000 to 2011. A nonparametric basin-scale trend test of annual data shows a clear increasing trend for runoff, air temperature, and precipitation in the headwater catchment. We propose a copula-based approach, for studying the statistical dependence structure of hydro-climatic variables. We also constructed a two-dimensional tail estimator, to describe the nature of the tail dependence parameter, and as a means of studying its asymptotic properties. Tail dependence parameters demonstrate that air temperature has the greatest influence on runoff, followed by snow cover, precipitation, and evapotranspiration. Step-wise changes were noted to occur in the statistical dependence structure in dependence relationships, due to changes in major climate variables. Snow cover recession in the headwater catchment is consistent with the warming trend recorded by meteorological stations, but regional climate warming does not always result in snow cover reduction, owing to increased precipitation in regions such as the Aksu River basin, where a post-2000 increase in the snow cover area may have contributed to increased runoff, against a background of regional warming and wetting post-2000. Increased air temperature and precipitation, which resulted in increased runoff within the mountainous region, give rise to snowmelt and glacier-melt. Results from this study provide useful information for the planning and management of water resources in the study area.

Information Spreading in a Large Population of Active Transmitters and Passive Receivers

This paper discusses a simple stochastic model for the spread of messages in a large population with two types of individuals: transmitters and receivers. Transmitters, after receiving the message, start spreading copies of the message to their neighbors. Receivers may receive the message but will never spread it further. We derive approximations of the broadcast time and the first passage times of selected individuals in populations of size tending to infinity. These approximations explain how much the fact that only a fraction of the individuals are transmitters slows down the propagation of information. Our results also sharply characterize the statistical dependence structure of first passage times using Gumbel and logistic distributions of extreme value statistics.

On bid-price controls for network revenue management

We consider a network revenue management problem and advance its dual formulation. The dual formulation reveals that the (optimal) shadow price of capacity forms a nonnegative martingale. This result is proved under minimal assumptions on network topology and stochastic nature of demand, allowing an arbitrary statistical dependence structure across time and products. Next, we consider a quadratic perturbation of the network revenue management problem and show that a simple (perturbed) bid-price control is optimal for the perturbed problem; and it is $\varepsilon$-optimal for the original network revenue management problem. Finally, we consider a predictable version of this control, where the bid prices used in the current period are last updated in the previous period, and provide an upper bound on its optimality gap in terms of the (quadratic) variation of demand. Using this upper bound we show that there exists a near-optimal such control in the usual case when periods are small compared to the planning horizon provided that either demand or the incremental information arriving during each period is small. We establish the martingale property of the (near) optimal bid prices in both settings. The martingale property can have important implications in practice as it may offer a tool for monitoring the revenue management systems.

Derivation of low flow distribution functions using copulas

Derivation of low flow distribution using recession functions has been introduced in previous studies, but without taking into consideration the statistical dependence structure between the characteristics of low flow event, i.e. the duration of dry spell t and the recession parameter k. Low flow data of three basins in China with different climates demonstrate that statistical dependence actually exists between t and k. A copula-based derived distribution is proposed in this paper to take full account of this internal dependence within the low flow event. The proposed derived distribution can be flexibly constructed using a wide variety of copula functions and marginal distributions. Four types of copula functions (i.e. Student, Clayton, Gumbel, and Frank), each with twelve combinations of marginal distributions, are all employed to derive low flow distributions to find out which component, copula function or marginal distribution, has the most impact on the performance of derived low flow distributions in fitting the observed data. It turns out that the capability of this copula-based derived distribution is strongly influenced by the choice of marginal distribution, while different copula functions have more than negligible impacts on the tails’ goodness-of-fit. Student copula is preferred to model the chosen (t, k) samples with both lower and upper tail dependence. But the copula-based derived distribution is not recommended to describe low flow samples with long lower tails. The performance of the copula-based derived distributions is compared with that of the derived truncated Weibull distribution whose parameters are also process-oriented but without considering the statistical dependence structure of (t, k) in low flow events. The results highlight that the copula-based derived distribution is more flexible and can more reasonably describe both the upper and lower tails of low flow series than the derived truncated Weibull distribution. Two traditional fitted distributions, fitted truncated Weibull distribution and fitted Pearson Type III distribution, are also applied to describe the low flow series to evaluate the capability of the copula-based derived distribution. The fitted Pearson Type III distribution always provides highest accuracy, while copula-based derived distributions perform comparably given the appropriate marginal distributions and copula function. In general, the copula-based derived distribution can be a potential attractive alternative in low flow frequency analysis, for it can be used in studying the impacts of climate change and human activities on the frequency of low flows.

A copula approach on the dynamics of statistical dependencies in the US stock market

We analyze the statistical dependence structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange’s TAQ database. Instead of using a given parametric copula with a predetermined shape, we study the empirical pairwise copula directly. We find that the shape of this copula resembles the Gaussian copula to some degree, but exhibits a stronger tail dependence, for both correlated and anti-correlated extreme events. By comparing the tail dependence dynamically to the market’s average correlation level as a commonly used quantity we disclose the average level of error of the Gaussian copula, which is implied in the calculation of many correlation coefficients.

Electrocardiographic and Hemodynamic Effects of Intravenous Infusion of Bupivacaine, Ropivacaine, Levobupivacaine, and Lidocaine In Anesthetized Ewes

Neural blockade techniques are associated with a risk of acute cardiac toxicity after accidental intravenous (IV) injection of local anesthetics. The aim of this study was to compare electrocardiographic (ECG) and hemodynamic (HEM) effects induced by IV infusion of local anesthetics in an anesthetized ewe model. Thirty-two anesthetized ewes received IV bupivacaine (BUPI), ropivacaine (ROPI), or levobupivacaine (S-BUPI) at an equimolar dose, or lidocaine (LIDO) at a 3-fold higher rate (n = 8 in each group). RR, PR, QRS, and QT intervals (QTc), changes (Delta) in systolic and diastolic arterial pressure (SAP and DAP), and in myocardial contractility (dP/dt), were assessed every 30 seconds for 7 minutes. From main ECG variables (RR, PR, QRS, QT), we proposed to use multiple correspondence analysis and hierarchical ascending classification to explore the structure of statistical dependencies among those measurements, and to determine the different patterns of ECG and HEM changes induced by infusion of BUPI, ROPI, S-BUPI, and LIDO. Graphic representation of multiple correspondence analysis associated BUPI with the most pronounced modifications in ECG and HEM variables, followed by in decreasing order ROPI, S-BUPI, and LIDO. Comparisons of clusters identified by hierarchical ascending classification confirmed this classification for ECG variables. Ventricular tachycardia occurred only in the BUPI group. In our anesthetized ewe model, high dose IV infusion of BUPI induced the most marked changes in RR, PR, QRS, QT, QTc intervals, DeltaSAP, and DeltadP/dt. ROPI altered ECG variables less than BUPI but more than S-BUPI. LIDO was associated with the smallest changes.

From Anatomic Standardization Analysis of Perfusion SPECT Data to Perfusion Pattern Modeling: Evidence of Functional Networks in Healthy Subjects and Temporal Lobe Epilepsy Patients 1

In the general context of perfusion pattern modeling from single-photon emission computed tomographic (SPECT) data, the purpose of this study is to characterize interindividual functional variability and functional connectivity between anatomic structures in a set of SPECT data acquired from a homogeneous population of subjects. From volume of interest (VOI)-perfusion measurements performed on anatomically standardized SPECT data, we proposed to use correspondence analysis (CA) and hierarchical clustering (HC) to explore the structure of statistical dependencies among these measurements. The method was applied to study the perfusion pattern in two populations of subjects; namely, SPECT data from 27 healthy subjects and ictal SPECT data from 10 patients with mesio-temporal lobe epilepsy (MTLE). For healthy subjects, anatomic structures showing statistically dependent perfusion patterns were classified into four groups; namely, temporomesial structures, internal structures, posterior structures, and remaining cortex. For patients with MTLE, they were classified as temporomesial structures, surrounding temporal structures, internal structures, and remaining cortex. Anatomic structures of each group showed similar perfusion behavior so that they may be functionally connected and may belong to the same network. Our main result is that the temporal pole and lenticular nucleus seemed to be highly relevant to characterize ictal perfusion in patients with MTLE. This exploratory analysis suggests that a network involving temporal structures, lenticular nucleus, brainstem, and cerebellum seems to be involved during MTLE seizures. CA followed by HC is a promising approach to explore brain perfusion patterns from SPECT VOI measurements.