Multivariate Observations Research Articles

Data-adaptive harmonic analysis and modeling of solar wind-magnetosphere coupling

The solar wind-magnetosphere coupling is studied by new data-adaptive harmonic decomposition (DAHD) approach for the spectral analysis and inverse modeling of multivariate time observations of complex nonlinear dynamical systems. DAHD identifies frequency-based modes of interactions in the combined dataset of Auroral Electrojet (AE) index and solar wind forcing. The time evolution of these modes can be very efficiently simulated by using systems of stochastic differential equations (SDEs) that are stacked per frequency and formed by coupled Stuart-Landau oscillators. These systems of SDEs capture the modes' frequencies as well as their amplitude modulations, and yield, in turn, an accurate modeling of the AE index' statistical properties.

Multivariate Regression with Gross Errors on Manifold-Valued Data.

We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly corrupted manifold-valued responses, a bottleneck issue commonly encountered in practical scenarios. Our model first takes a correction step on the grossly corrupted responses via geodesic curves on the manifold, then performs multivariate linear regression on the corrected data. This results in a nonconvex and nonsmooth optimization problem on Riemannian manifolds. To this end, we propose a dedicated approach named PALMR, by utilizing and extending the proximal alternating linearized minimization techniques for optimization problems on euclidean spaces. Theoretically, we investigate its convergence property, where it is shown to converge to a critical point under mild conditions. Empirically, we test our model on both synthetic and real diffusion tensor imaging data, and show that our model outperforms other multivariate regression models when manifold-valued responses contain gross errors, and is effective in identifying gross errors.

Robust Multi-Variate Temporal Features of Multi-Variate Time Series

Many applications generate and/or consume multi-variate temporal data, and experts often lack the means to adequately and systematically search for and interpret multi-variate observations. In this article, we first observe that multi-variate time series often carry localized multi-variate temporal features that are robust against noise. We then argue that these multi-variate temporal features can be extracted by simultaneously considering, at multiple scales, temporal characteristics of the time series along with external knowledge , including variate relationships that are known a priori. Relying on these observations, we develop data models and algorithms to detect robust multi-variate temporal (RMT) features that can be indexed for efficient and accurate retrieval and can be used for supporting data exploration and analysis tasks. Experiments confirm that the proposed RMT algorithm is highly effective and efficient in identifying robust multi-scale temporal features of multi-variate time series.

High dimensional efficiency with applications to change point tests

This paper rigourously introduces the asymptotic concept of high dimensional efficiency which quantifies the detection power of different statistics in high dimensional multivariate settings. It allows for comparisons of different high dimensional methods with different null asymptotics and even different asymptotic behavior such as extremal-type asymptotics. The concept will be used to understand the power behavior of different test statistics as the performance will greatly depend on the assumptions made, such as sparseness or denseness of the signal. The effect of misspecification of the covariance on the power of the tests is also investigated, because in many high dimensional situations estimation of the full dependency (covariance) between the multivariate observations in the panel is often either computationally or even theoretically infeasible. The theoretic quantification by the theory is accompanied by simulation results which confirm the theoretic (asymptotic) findings for surprisingly small samples. The development of this concept was motivated by, but is by no means limited to, high-dimensional change point tests. It is shown that the concept of high dimensional efficiency is indeed suitable to describe small sample power.

Probabilistic Forecast for Multiple Wind Farms Based on Regular Vine Copulas

The uncertain nature of wind power causes difficulties in power system operation scheduling. Probabilistic descriptions of the uncertainty have been studied for decades. However, probabilistic forecasts designed for the regional multiple wind farms are few. Although the traditional methods for the single wind farm can still be used, they have the limitations in capturing the spatial correlations among wind farms, and they are less robust when multivariate observations are not so complete. To improve the forecast quality in this case, we combine the multivariate distribution modeling and probabilistic forecasts in this paper. An advanced model—the regular vine copula, which can describe the wind farms’ dependence structure precisely and flexibly with various bivariate copulas as blocks, is used in this paper. Enough simulation data can be generated from the model, which can be easily used to form the conditional forecast distributions under multiple forecast conditions. A case of 10 wind farms in East China has been used to compare the proposed method with its competitors. The results showed the method's advantages of providing reliable and sharp forecast intervals, especially in the case with limited observations available.

Mass volume curves and anomaly ranking

This paper aims at formulating the issue of ranking multivariate unlabeled observations depending on their degree of abnormality as an unsupervised statistical learning task. In the 1-d situation, this problem is usually tackled by means of tail estimation techniques: univariate observations are viewed as all the more ‘abnormal’ as they are located far in the tail(s) of the underlying probability distribution. It would be desirable as well to dispose of a scalar valued ‘scoring’ function allowing for comparing the degree of abnormality of multivariate observations. Here we formulate the issue of scoring anomalies as a M-estimation problem by means of a novel functional performance criterion, referred to as the Mass Volume curve (MV curve in short), whose optimal elements are strictly increasing transforms of the density almost everywhere on the support of the density. We first study the statistical estimation of the MV curve of a given scoring function and we provide a strategy to build confidence regions using a smoothed bootstrap approach. Optimization of this functional criterion over the set of piecewise constant scoring functions is next tackled. This boils down to estimating a sequence of empirical minimum volume sets whose levels are chosen adaptively from the data, so as to adjust to the variations of the optimal MV curve, while controlling the bias of its approximation by a stepwise curve. Generalization bounds are then established for the difference in sup norm between the MV curve of the empirical scoring function thus obtained and the optimal MV curve.

Forecasting Market States

We propose a novel methodology to define, analyse and forecast market states. In our approach market states are identified by a reference sparse precision matrix and a vector of expectation values. In our procedure, each multivariate observation is associated to a given market state accordingly to a penalized likelihood maximization. The procedure is made computationally very efficient and can be used with a large number of assets. We demonstrate that this procedure successfully classifies different states of the markets in an unsupervised manner. In particular, we describe an experiment with one hundred log-returns and two states in which the methodology automatically associates one state to periods with average positive returns and the other state to periods with average negative returns, therefore discovering spontaneously the common classification of 'bull' and 'bear' markets. In another experiment, with again one hundred log-returns and two states, we demonstrate that this procedure can be efficiently used to forecast off-sample future market states with significant prediction accuracy. This methodology opens the way to a range of applications in risk management and trading strategies where the correlation structure plays a central role.

Variational inference for probabilistic Poisson PCA

Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to understand the co-variations between these species. The Gaussian setting provides a canonical way to model such dependencies, but does not apply in general. We consider here the multivariate exponential family framework for which we introduce a generic model with multivariate Gaussian latent variables. We show that approximate maximum likelihood inference can be achieved via a variational algorithm for which gradient descent easily applies. We show that this setting enables us to account for covariates and offsets. We then focus on the case of the Poisson-lognormal model in the context of community ecology.

Multivariate normal estimation: the case (n < p)

ABSTRACTEstimation in the multivariate context when the number of observations available is less than the number of variables is a classical theoretical problem. In order to ensure estimability, one has to assume certain constraints on the parameters. A method for maximum likelihood estimation under constraints is proposed to solve this problem. Even in the extreme case where only a single multivariate observation is available, this may provide a feasible solution. It simultaneously provides a simple, straightforward methodology to allow for specific structures within and between covariance matrices of several populations. This methodology yields exact maximum likelihood estimates.

Topics in Inclusive Design for the Graduate Human Factors Engineering Curriculum

The confluence of demographic trends in aging and disability prevalence, increased expectations among workers and consumers with and without impairments, and greater reliance on complex yet pervasive technologies (e.g., automation, internet of things) has resulted in an increased emphasis on designing for human-system performance and accommodation across the full spectrum of human abilities. Inclusive design or universal design (UD) is one of the few user-centered design paradigms that advocate consideration for the full spectrum of human abilities, including individuals with and without disabilities. A graduate-level course was developed and implemented to introduce ergonomics and human factors students to the UD paradigm and to UD goals and principles using select academic and non-academic readings, and assignments related to multivariate statistics, field observations, and design of experiments. The course placed an emphasis on the fundamentals and research base in ergonomics in relation to UD research and practice, viz., topics related to variability in human functioning and performance associated with anthropometry, biomechanics, perception and cognition. Alongside the motivations for the course, this paper provides an overview of the course objectives, topics covered, and some early lessons learned.

Multivariate anomaly detection for Earth observations: a comparison of algorithms and feature extraction techniques

Abstract. Today, many processes at the Earth's surface are constantly monitored by multiple data streams. These observations have become central to advancing our understanding of vegetation dynamics in response to climate or land use change. Another set of important applications is monitoring effects of extreme climatic events, other disturbances such as fires, or abrupt land transitions. One important methodological question is how to reliably detect anomalies in an automated and generic way within multivariate data streams, which typically vary seasonally and are interconnected across variables. Although many algorithms have been proposed for detecting anomalies in multivariate data, only a few have been investigated in the context of Earth system science applications. In this study, we systematically combine and compare feature extraction and anomaly detection algorithms for detecting anomalous events. Our aim is to identify suitable workflows for automatically detecting anomalous patterns in multivariate Earth system data streams. We rely on artificial data that mimic typical properties and anomalies in multivariate spatiotemporal Earth observations like sudden changes in basic characteristics of time series such as the sample mean, the variance, changes in the cycle amplitude, and trends. This artificial experiment is needed as there is no gold standard for the identification of anomalies in real Earth observations. Our results show that a well-chosen feature extraction step (e.g., subtracting seasonal cycles, or dimensionality reduction) is more important than the choice of a particular anomaly detection algorithm. Nevertheless, we identify three detection algorithms (k-nearest neighbors mean distance, kernel density estimation, a recurrence approach) and their combinations (ensembles) that outperform other multivariate approaches as well as univariate extreme-event detection methods. Our results therefore provide an effective workflow to automatically detect anomalies in Earth system science data.

SURE estimates under dependence and heteroscedasticity

The multivariate Bayesian hierarchical model with independent means has been studied extensively and is widely used in practice. In contrast, the case of dependent means has received scant attention, even though multivariate observations are often correlated. In this paper, we investigate a multivariate heteroscedastic Bayesian hierarchical model in which an informative prior with equicorrelated means is assumed. We estimate the mean vector by the shrinkage estimator based on Stein’s unbiased risk estimation (SURE). It is shown that the squared error loss of the SURE estimator is close to that of an oracle estimator as the number of means grows. Our SURE estimator includes the SURE estimator under independence considered by Xie et al. (2012) as a special case. The finite-sample performance of our estimator is explored via simulations and two real data sets are used for illustration purposes.

A Quality Control Method for Wind Profiler Observations toward Assimilation Applications

AbstractA wind profiler network with a total of 65 profiling radar systems was operated by the China Meteorological Observation Center (MOC) of the China Meteorological Administration (CMA) until July 2015. In this study, a quality control procedure is constructed to incorporate the profiler data from the wind-profiling network into the local data assimilation and forecasting systems. The procedure applies a blacklisting check that removes stations with gross errors and an outlier check that rejects data with large deviations from the background. As opposed to the biweight method, which has been commonly implemented in outlier elimination for univariate observations, the outlier elimination method is developed based on the iterated reweighted minimum covariance determinant (IRMCD) for multivariate observations, such as wind profiler data. A quality control experiment is performed separately for subsets containing profiler data tagged with/without rain flags in parallel every 0000 and 1200 UTC from 20 June to 30 September 2015. The results show that with quality control, the frequency distributions of the differences between the observations and the model background meet the requirements of a Gaussian distribution for data assimilation. A further intensive assessment of each quality control step reveals that the stations rejected by the blacklisting contained poor data quality and that the IRMCD rejects outliers in a robust and physically reasonable manner. Detailed comparisons between the IRMCD and the biweight method are performed, and the IRMCD is demonstrated to be more efficient and more comprehensive regarding the dataset used in this study.

‘Size’ and ‘shape’ in the measurement of multivariate proximity

Summary Ordination and clustering methods are widely applied to ecological data that are non‐negative, for example, species abundances or biomasses. These methods rely on a measure of multivariate proximity that quantifies differences between the sampling units (e.g. individuals, stations, time points), leading to results such as: (i) ordinations of the units, where interpoint distances optimally display the measured differences; (ii) clustering the units into homogeneous clusters or (iii) assessing differences between pre‐specified groups of units (e.g. regions, periods, treatment–control groups). These methods all conceal a fundamental question: To what extent are the differences between the sampling units, computed according to the chosen proximity function, capturing the ‘size’ in the multivariate observations, or their ‘shape’? ‘Size’ means the overall level of the measurements: for example, some samples contain higher total abundances or more biomass, others less. ‘Shape’ means the relative levels of the measurements: for example, some samples have different relative abundances, i.e. different compositions. To answer this question, several well‐known proximity measures are considered and applied to two datasets, one of which is used in a simulation exercise where ‘shape’ differences have been eliminated by randomization. For any dataset and any proximity measure, a quantification is achieved of the proportion of ‘size’ variance and ‘shape’ variance that the measure is capturing, as well as the proportion of variance that confounds ‘size’ and ‘shape’ together. The results consistently show that the Bray–Curtis coefficient incorporates both ‘size’ and ‘shape’ differences, to varying degrees. These two components are thus always confounded by this proximity measure in the determination of ordinations, clusters, group comparisons and relations to environmental variables. There are several implications of these results, the main one being that researchers should be aware of this issue when they choose a proximity measure. They should compute the ‘size’ and ‘shape’ components for their particular datasets, as this can radically affect the interpretation of their results. It is recommended to separate these components: analysing total abundances or other measures of ‘size’ by univariate methods, and using multivariate analysis on the relative abundances where size has been specifically excluded.

A Bayesian Multivariate Functional Dynamic Linear Model

ABSTRACT We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data—functional, time dependent, and multivariate components—we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time–frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online.

Selective overview of forward selection in terms of robust correlations

ABSTRACTForward selection (FS) is a very effective variable selection procedure for selecting a parsimonious subset of covariates from a large number of candidate covariates. Detecting the type of outlying observations, such as vertical outliers or leverage points, and the FS procedure are inseparable problems. For robust variable selection, a crucial issue is whether the outliers are univariate, bivariate, or multivariate. This paper uses a consistent robust multivariate dispersion estimator to obtain robust correlation estimators used to establish robust forward selection (RFS) procedures that outperform methods that use robust bivariate correlations. The usefulness of our proposed procedure is studied with a numerical example and a simulation study. The result shows the proposed method has scalability and the ability to deal with univariate, bivariate and multivariate outlying observations including leverage points or vertical outliers, and the new method outperforms previously published methods of RFS.

Discriminant analysis by quantile regression with application on the climate change problem

With the widespread use of discriminant analysis in various fields, e.g. multivariate data, regression models, and times series observations, this paper introduces a quantile regression statistic to classify time series data into a certain category. Results show that the misclassification probability of the discriminant statistic converges to zero as the sample size tends to infinity. We also evaluate the performance of the statistics when the categories are contiguous. We apply the proposed method in quantile autoregression to a dataset of the monthly mean maximum temperature at Melbourne, Australia from January 1944 to December 2015. The findings illuminate interesting features of climate change and allow us to check the change at each quantile of the innovation distribution. Because the proposed method is general, there are many potential applications of this approach.

Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study

Many scientific studies measure different types of high-dimensional signals or images from the same subject, producing multivariate functional data. These functional measurements carry different types of information about the scientific process, and a joint analysis that integrates information across them may provide new insights into the underlying mechanism for the phenomenon under study. Motivated by fluorescence spectroscopy data in a cervical pre-cancer study, a multivariate functional response regression model is proposed, which treats multivariate functional observations as responses and a common set of covariates as predictors. This novel modeling framework simultaneously accounts for correlations between functional variables and potential multi-level structures in data that are induced by experimental design. The model is fitted by performing a two-stage linear transformation—a basis expansion to each functional variable followed by principal component analysis for the concatenated basis coefficients. This transformation effectively reduces the intra- and inter-function correlations and facilitates fast and convenient calculation. A fully Bayesian approach is adopted to sample the model parameters in the transformed space, and posterior inference is performed after inverse-transforming the regression coefficients back to the original data domain. The proposed approach produces functional tests that flag local regions on the functional effects, while controlling the overall experiment-wise error rate or false discovery rate. It also enables functional discriminant analysis through posterior predictive calculation. Analysis of the fluorescence spectroscopy data reveals local regions with differential expressions across the pre-cancer and normal samples. These regions may serve as biomarkers for prognosis and disease assessment.

Compositional analysis of trade flows structure

Statistical analysis of trade flows structure can significantly help to reveal or to confirm important macroeconomic phenomena. Because of relative character of these multivariate observations, application of standard multivariate methods directly to raw data can lead to meaningless results, affected by trade sizes of different countries. As a way out, it is proposed to employ the logratio methodology that is able to capture interesting features through logratios between compositional parts. Particularly, the perturbation operation together with clr coefficients for coordinate representation of compositions seem to be easy to handle and to interpret for the purpose. Popular exploratory tools, principal component analysis and PARAFAC modeling of threeway data, resulting from a long-term study of the export/import structure, are applied in the compositional context for data from OECD and WIOD databases. The results show that the logratio methodology enables to reveal interesting features of world trade flows and thus provides a preferable alternative to existing exploratory tools.

Comparison of Metazoan Parasite Diversity in Catfishes Within and Outside the Big Thicket National Preserve, Texas, U.S.A.

Species richness and composition of the metazoan parasite communities of 2 ictalurid catfishes (yellow bullhead [Ameiurus natalis] and channel catfish [Ictalurus punctatus]) were compared from within the Big Thicket National Preserve in southeastern Texas, U.S.A., to areas outside the preserve. Ninety-five fishes were sampled from 2009 to 2013 from 6 sites each inside and outside the Preserve, and 31 species of parasites were recovered (27 species from inside and 14 species from outside). Comparison of species accumulation curves utilizing recently developed methods demonstrated significant differences in the species richness and composition, the abundance distributions for parasite communities as a whole, or both, and of the community of channel catfish considered alone. Additional univariate and multivariate analyses and observations confirmed significant differences in the species composition and abundance of these parasite communities. The parasite community inside the Preserve is dominated by adult endohelminths representing both ictalurid specialists that are either absent or less abundant outside the Preserve. Additionally, generalist parasites more commonly parasitizing other fishes were more speciose and abundant inside the Preserve. The differences observed in the present investigation suggest that the waters of the Big Thicket National Preserve harbor more diverse and abundant fish, invertebrate communities, or both, thus leading to higher diversity and abundance of their parasite communities.