Oscillation analysis using optical flow: Application to an EUV movie of the solar corona

Movies of the solar corona in Extreme UltraViolet (EUV) bandpasses exhibit complex patterns of magnetically structured plasma features surrounding the solar photosphere. Among the various phenomena to be observed in the EUV movies, coronal oscillations are an essential process for determining physical parameters of the plasma. In this paper we demonstrate the ability of our motion estimation algorithm to explore and analyse the oscillating motions of coronal loops present in EUV image sequences. The motion fields of each image pair in the sequence are estimated; selected features are tracked using the motion estimation to form trajectories. The oscillating features are then selected from the Morlet wavelet analysis of the trajectories that provides parameters such as local oscillation period. The proposed method will be particularly useful to process datasets expected from new solar missions.     

Simulation of the p-generalized Gaussian distribution

In this paper, we introduce the p-generalized polar methods for the simulation of the p-generalized Gaussian distribution. On the basis of geometric measure representations, the well-known Box–Muller method and the Marsaglia–Bray rejecting polar method for the simulation of the Gaussian distribution are generalized to simulate the p-generalized Gaussian distribution, which fits much more flexibly to data than the Gaussian distribution and has already been applied in various fields of modern sciences. To prove the correctness of the p-generalized polar methods, we give stochastic representations, and to demonstrate their adequacy, we perform a comparison of six simulation techniques w.r.t. the goodness of fit and the complexity. The competing methods include adapted general methods and another special method. Furthermore, we prove stochastic representations for all the adapted methods.     

Dynamic model-based clustering for spatio-temporal data

In many research fields, scientific questions are investigated by analyzing data collected over space and time, usually at fixed spatial locations and time steps and resulting in geo-referenced time series. In this context, it is of interest to identify potential partitions of the space and study their evolution over time. A finite space-time mixture model is proposed to identify level-based clusters in spatio-temporal data and study their temporal evolution along the time frame. We anticipate space-time dependence by introducing spatio-temporally varying mixing weights to allocate observations at nearby locations and consecutive time points with similar cluster’s membership probabilities. As a result, a clustering varying over time and space is accomplished. Conditionally on the cluster’s membership, a state-space model is deployed to describe the temporal evolution of the sites belonging to each group. Fully posterior inference is provided under a Bayesian framework through Monte Carlo Markov chain algorithms. Also, a strategy to select the suitable number of clusters based upon the posterior temporal patterns of the clusters is offered. We evaluate our approach through simulation experiments, and we illustrate using air quality data collected across Europe from 2001 to 2012, showing the benefit of borrowing strength of information across space and time.     

Use of estimated fractal dimension in model identification for time series

A fractal and its dimension has been a subject of great mathematical interest since the publication of Mandelbrot's manifestoes (1977, 1982). This paper discusses some empirical results indicating the potential usefulness of estimated fractal dimension in testing for white noise. These tests are applied for model identification in time series, and results for previously analyzed data are provided. A method for fractal interpolation of a continuous process from a finite number of observations is discussed, as well as some future research directions.     

Segmental dynamic factor analysis for time series of curves

A new approach is introduced in this article for describing and visualizing time series of curves, where each curve has the particularity of being subject to changes in regime. For this purpose, the curves are represented by a regression model including a latent segmentation, and their temporal evolution is modeled through a Gaussian random walk over low-dimensional factors of the regression coefficients. The resulting model is nothing else than a particular state-space model involving discrete and continuous latent variables, whose parameters are estimated across a sequence of curves through a dedicated variational Expectation-Maximization algorithm. The experimental study conducted on simulated data and real time series of curves has shown encouraging results in terms of visualization of their temporal evolution and forecasting.     

Longitudinal models for polytomous responses

Recent work by Miller and Landis (1991) discusses generalized variance component models for polytomous responses. This work is adapted to longitudinal models for repeated measures of individuals having polytomous responses. In this setting, individuals are considered to be “clusters”. The resulting simplifications are discussed. First, each response has a multinomial distribution with N=l. Second, observed cluster proportions in the variance component estimates must be replaced by their expectations. This technique accommodates patients with missing data in a sequence of repeated observations.     

Non-parametric smoothing of spatio-temporal point processes

This paper develops adaptive non-parametric modelings for earthquake data. Non-parametric techniques are particularly suitable for space–time point processes, however they must be adapted to deal with the non-stationarity of seismic phenomena. By this we mean changes in the spatial and temporal pattern of seismic occurrences. A set of non-parametric tests, kernel density and regression estimators are proposed to study the space–time evolution of earthquakes. The implied solutions, by respecting the unidirectional nature of time and minimizing prediction errors, are naturally oriented to forecasting. An extensive application to the Northern California Earthquake Catalog (NCEC) data-set, starting from 1930, illustrates and checks the approach.     

On reliability estimation based on fuzzy lifetime data

Real lifetime data are never precise numbers but more or less non-precise, also called fuzzy. This kind of imprecision is connected with all measurement results of continuous variables, therefore also with time observations. Imprecision is different from errors and variability. Therefore estimation methods for reliability characteristics have to be adapted to the situation of fuzzy lifetimes in order to obtain realistic results.     

Inférence statistique dans les processus stochastiques: Aperçu historique

The study of statistical inference for stochastic processes has evolved along two paths. Some problems related to particular processes have been studied, and also some trials to extend general results obtained for independent identically distributed random variables have been made. We retrace the first main contributions, evaluate their influence, and give an idea of the evolution of the research in the field of statistical inference made with observations coming from a stochastic process.     

Computational approximation of the likelihood ratio for testing the existence of change-points in a heteroscedastic series

In this work, we present a computational method to approximate the occurrence of the change-points in a temporal series consisting of independent and normally distributed observations, with equal mean and two possible variance values. This type of temporal series occurs in the investigation of electric signals associated to rhythmic activity patterns of nerves and muscles of animals, in which the change-points represent the actual moments when the electrical activity passes from a phase of silence to one of activity, or vice versa. We confront the hypothesis that there is no change-point in the temporal series, against the alternative hypothesis that there exists at least one change-point, employing the corresponding likelihood ratio as the test statistic; a computational implementation of the technique of quadratic penalization is employed in order to approximate the quotient of the logarithmic likelihood associated to the set of hypotheses. When the null hypothesis is rejected, the method provides estimations of the localization of the change-points in the temporal series. Moreover, the method proposed in this work employs a posteriori processing in order to avoid the generation of relatively short periods of silence or activity. The method is applied to the determination of change-points in both experimental and synthetic data sets; in either case, the results of our computations are more than satisfactory.     

Approximating likelihoods for large spatial data sets

Summary.  Likelihood methods are often difficult to use with large, irregularly sited spatial data sets, owing to the computational burden. Even for Gaussian models, exact calculations of the likelihood for n observations require O ( n ³) operations. Since any joint density can be written as a product of conditional densities based on some ordering of the observations, one way to lessen the computations is to condition on only some of the 'past' observations when computing the conditional densities. We show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation. Previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating. Through theoretical, numerical and practical examples, we show that there can often be considerable benefit in conditioning on some distant observations as well.     

VisIOT:经济产业结构关联可视分析

随着经济统计范畴的精细化以及统计过程的规范化，能够表现产业部门关联关系的投入产出表（Input-Output Table，IOT）数据日益呈现复杂的结构特性。传统的统计分析软件和方法形式单一且传达信息有限，面对结构关系复杂且动态演化的IOT数据，难以有效分析和探索其中复杂的关联模式和时序变化特征。为此，本文设计面对IOT数据分析的经济产业结构关联特征可视化工具——VisIOT。首先设计双向力导向图描述国民经济结构关联网络，并对网络中的顶点和边进行属性映射；然后构建时序矩阵图，直观地展示IOT数据差异，并按照时间顺序依次嵌入时序IOT数据；其次利用部门间的经济技术联系优化模块度算法，发掘经济产业结构关联网络中隐含的社区特征，有效支持关联紧密的社区结构的交互式分析和提取；再次设计社区时序演变图展示社区结构特征的时序演化规律，借助交叉优化算法和前后向的扫描算法，优化部门排列顺序，减少部门交叉，帮助用户有效捕捉社区结构的稳定性；最后有效设计交互方案关联可视化界面，实现经济产业结构关联可视分析系统。本文利用真实的IOT数据进行实例分析与验证，结果表明本文设计的VisIOT系统能够帮助用户快速识别和感知IOT数据中隐含的关联特征及其时序变化规律。     

Fractal Function Estimation via Wavelet Shrinkage

In scientific studies objects are often very rough. Mathematically these rough objects are modelled by fractal functions, and the fractal dimension is usually used to measure their roughness. This paper investigates fractal function estimation by wavelet shrinkage. It is shown that wavelet shrinkage can estimate fractal functions with their fractal dimensions virtually preserved.     

The specification of vector autoregressive moving average models

In this paper we propose a new identification method based on the residual white noise autoregressive criterion (Pukkila et al., 1990) to select the order of VARMA structures. Results from extensive simulation experiments based on different model structures with varying number of observations and number of component series are used to demonstrate the performance of this new procedure. We also use economic and business data to compare the model structures selected by this order selection method with those identified in other published studies.     

Spatio-temporal change-point modeling

There is by now a substantial literature on spatio-temporal modeling. However, to date, there exists essentially no literature which addresses the issue of process change from a certain time. In fact, if we look at change points for purely time series data, the customary form is to propose a model involving a mean or level shift. We see little attempting to capture a change in association structure. Part of the concern is how to specify flexible ways to bridge the association across the time point and still ensure that a proper joint distribution has been defined for all of the data. Introducing a spatial component evidently adds further complication. We want to allow for a change-point reflecting change in both temporal and spatial association. In this paper we propose a constructive, flexible model formulation through additive specifications. We also demonstrate how computational concerns benefit from the availability of temporal order. Finally, we illustrate with several simulated datasets to examine the capability of the model to detect different types of structural changes.     

Unaliasing of aliased line component frequencies

This paper is concerned with undoing aliasing effects, which arise from discretely sampling a continuous‐time stochastic process. Such effects are manifested in the frequency‐domain relationships between the sampled and original processes. The authors describe a general technique to undo aliasing effects, given two processes, one being a time‐delayed version of the other. The technique is based on the observations that certain phase information between the two processes is unaffected by sampling, is completely determined by the (known) time delay, and contains sufficient information to undo aliasing effects. The authors illustrate their technique with a simulation example. The theoretical model is motivated by the helioseismological problem of determining modes of solar pressure waves. The authors apply their technique to solar radio data, and conclude that certain low‐frequency modes known in the helioseismology literature are likely the result of aliasing effects. The Canadian Journal of Statistics 38: 116–135; 2010 © 2010 Statistical Society of Canada     

Marginally restricted D-optimal designs for correlated observations

Two practical degrees of complexity may arise when designing an experiment for a model of a real life case. First, some explanatory variables may not be under the control of the practitioner. Secondly, the responses may be correlated. In this paper three real life cases in this situation are considered. Different covariance structures are studied and some designs are computed adapting the theory of marginally restricted designs for correlated observations. An exchange algorithm given by Brimkulov's algorithm is also adapted to marginally restricted D–optimality and it is applied to a complex situation.     

Physically constrained spatiotemporal modeling: generating clear-sky constructions of land surface temperature from sparse,remotely sensed satellite data

Satellite remote-sensing is used to collect important atmospheric and geophysical data at various spatial resolutions, providing insight into spatiotemporal surface and climate variability globally. These observations are often plagued with missing spatial and temporal information of Earth''s surface due to (1) cloud cover at the time of a satellite passing and (2) infrequent passing of polar-orbiting satellites. While many methods are available to model missing data in space and time, in the case of land surface temperature (LST) from thermal infrared remote sensing, these approaches generally ignore the temporal pattern called the ‘diurnal cycle’ which physically constrains temperatures to peak in the early afternoon and reach a minimum at sunrise. In order to infill an LST dataset, we parameterize the diurnal cycle into a functional form with unknown spatiotemporal parameters. Using multiresolution spatial basis functions, we estimate these parameters from sparse satellite observations to reconstruct an LST field with continuous spatial and temporal distributions. These estimations may then be used to better inform scientists of spatiotemporal thermal patterns over relatively complex domains. The methodology is demonstrated using data collected by MODIS on NASA''s Aqua and Terra satellites over both Houston, TX and Phoenix, AZ USA.     

Classification of Higher-order Data with Separable Covariance and Structured Multiplicative or Additive Mean Models

Although devised in 1936 by Fisher, discriminant analysis is still rapidly evolving, as the complexity of contemporary data sets grows exponentially. Our classification rules explore these complexities by modeling various correlations in higher-order data. Moreover, our classification rules are suitable to data sets where the number of response variables is comparable or larger than the number of observations. We assume that the higher-order observations have a separable variance-covariance matrix and two different Kronecker product structures on the mean vector. In this article, we develop quadratic classification rules among g different populations where each individual has κth order (κ ≥2) measurements. We also provide the computational algorithms to compute the maximum likelihood estimates for the model parameters and eventually the sample classification rules.     

A Diagnostic Method for Principal Components Tests

The local influence method is adapted to testing hypotheses about principal components for investigating the influence of observations on the test statistic. Simultaneous perturbations on all observations are considered. The main diagnostic is the direction vector of the maximum slope of the surface formed by the perturbed test statistic. A perturbation is constructed whose result is the same as that of the influence function method. An example is given for illustration.