Designing Sampling Strategies for the Efficient Estimation of Parameterized Spatial Covariance Models

The data open sharing provides us opportunity to investigate mechanisms underlying autism spectrum disorder (ASD) by employing advanced techniques. In the current study, we employed structural covariance (SC) model to investigate the development of triple networks in ASD. Three hundred and seven ASD and 337 typical controls were collected and further classified into four distinct age cohorts. Night brain seeds belonging to default modal network, salience network, and central executive network were obtained. SC between those seeds, as well as its topological properties, was calculated for each group within each age cohort. Statistical analysis revealed that ASD had dynamic reconfigurations of SC of the triple networks, especially the right fronto-insular cortex. The results might indicate that ASD had specific mechanism within distinct age cohort. Additionally, the big data sharing, together with the SC modal, was able to facilitate understanding of the mechanism underlying ASD.

Mixture regression for longitudinal data based on joint mean–covariance model

Many psychological theories predict that cognitions, affect, action tendencies, and other variables change across time in mean level as well as in covariance structure. Often such changes are rather abrupt, because they are caused by sudden events. To capture such changes, one may repeatedly measure the variables under study for a single individual and examine whether the resulting multivariate time series contains a number of phases with different means and covariance structures. The latter task is challenging, however. First, in many cases, it is unknown how many phases there are and when new phases start. Second, often a rather large number of variables is involved, complicating the interpretation of the covariance pattern within each phase. To take up this challenge, we present switching principal component analysis (PCA). Switching PCA detects phases of consecutive observations or time points (in single subject data) with similar means and/or covariation structures, and performs a PCA per phase to yield insight into its covariance structure. An algorithm for fitting switching PCA solutions as well as a model selection procedure are presented and evaluated in a simulation study. Finally, we analyze empirical data on cardiorespiratory recordings.

Methods for repeated measures data analysis with missing values

Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function Z(x, t) observed repeatedly at times ti (i = 1, …, T) at a finite number of sampling stations xi (i = 1, 2, …, N) in the plane. Our analyses assume temporal stationarity but do not assume spatial stationarity (or isotropy). We analyze the spatial dispersions var(Z(xi, t) − Z(xj, t)) as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs (xi, xj ). The model is constructed in two steps. First, using nonmetric multidimensional scaling (MDS) we compute a two-dimensional representation of the sampling stations for which a monotone function of interpoint distances δij approximates the spatial dispersions. MDS transforms the problem into one for which the covariance structure, expressed in terms of spatial dispersions, is stationary and isotropic. Second, we compute thin-plate splines to provide smooth mappings of the geographic representation of the sampling stations into their MDS representation. The composition of this mapping f and a monotone function g derived from MDS yields a nonparametric estimator of var(Z(xa, t) − Z(xb, t)) for any two geographic locations xa and xb (monitored or not) of the form g(|f(xa ) − f(xb )|). By restricting the monotone function g to a class of conditionally nonpositive definite variogram functions, we ensure that the resulting nonparametric model corresponds to a nonnegative definite covariance model. We use biorthogonal grids, introduced by Bookstein in the field of morphometrics, to depict the thin-plate spline mappings that embody the nature of the anisotropy and nonstationarity in the sample covariance matrix. An analysis of mesoscale variability in solar radiation monitored in southwestern British Columbia demonstrates this methodology.

Nowadays, the Fast Fourier transform (FFT) has been widely adopted for harmonic analysis in power system. However, a direct application of FFT-based algorithms may bring about inaccurate results because of spectral leakage and picket-fence effects. In this paper, a high accuracy method based on the all-phase and interpolated FFT is presented for harmonic analysis. Firstly, the input signal is preprocessed to mitigate spectral leakage through all-phase. Secondly, the interpolation algorithm is adopted to eliminate the picket-fence effects. As a result, the analysis accuracy of the harmonic parameters has been greatly improved and the phase estimation is not biased. The formulas of amplitude, frequency and phase are also obtained based on all-phase and interpolated FFT. The simulation results reflect that this method can better meet the requirements of harmonic detection in power system.

Fast Fourier Transform (FFT) is used to obtain the Fourier spectrum of a periodic signal, but it is well known that special care must be taken to avoid severe distortions introduced by the sampling process. The major errors associated with this algorithm are spectral leakage and picket fence effect. This paper discusses the advancement in FFT algorithms for harmonic analysis in power system by applying windowed interpolation techniques. It is observed that the application of different WIFFT algorithms has different effects on the measuring accuracy. The advanced minimized sidelobe window (MSW) algorithm has better performance characteristics when compared to the conventional hanning and hamming windows adopted for harmonic analysis. By considering the practical harmonic data the hanning, hamming and MSW algorithms are validated using matlab programming. The simulation results demonstrate the effectiveness of hanning, hamming and MSW by considering the magnitude and phase angle error variations with respect to the harmonic order.

Spectral leakage and picket fence effect in Fourier transform will affect the accuracy of harmonic analysis under asynchronous sampling. To overcome this defect, a novel algorithm for power system harmonic analysis called Frequency Shifting and Filtering (FSF) algorithm is proposed in this paper. In this method, a reference signal is given to shift the frequency of original signal. And then the filter process based on iterative smoothing filter is adopted to eliminate the interference components. Finally, accurate results of harmonic parameters could be obtained by calculating the variations between original and frequency shifting signal. Simulation results have validated that the proposed algorithm can increase the accuracy of harmonic analysis efficiently.

The discrete Fourier transform (DFT) is still a widely used tool for analyzing and measuring both stationary and transient signals in power systems. However, the misapplications of DFT can lead to incorrect results caused by some problems, such as aliasing effect, spectral leakage, and picket-fence effect. This paper establishes a relationship between DFT-based spilled energy and harmonics/noninteger harmonics using the numerical induction method. Based on this study, a strategy of group-harmonics energy diffusion algorithm has been developed for both stationary and nonstationary harmonic/interharmonic evaluation in power systems. Especially, the frequency deviation range is used for frequency estimation, and the restored amplitude is used for retrieving dispersed amplitude. Accordingly, the harmonic/interharmonic frequency and its respective amplitude component can be accurately estimated using a simple mathematic computation. The numerical examples are presented to verify the performance of the proposed algorithm in terms of speed, accuracy, and efficiency.

The Discrete Fourier Transform (DFT) is still a widely-used tool for analyzing and measuring both stationary and transient signals in power systems. However, the misapplications of DFT can lead to incorrect results caused by some problems such as aliasing effect, spectral leakage and picket-fence effect. A strategy of Piecewise-overlapped Group-harmonic Energy Restoring (PGER) algorithm is developed for both stationary and non-stationary harmonic evaluation in power systems. The proposed algorithm can restore dispersing spectral leakage energy caused by the DFT, and thus retrieve the respective real harmonic value. Based on the piecewise-overlapped method, especially every time-varying harmonic can be extracted fast and accurately. The numerical examples are presented to verify the proposed algorithm in term of robust, fast and high-precision performance.

This paper presents a three-phase harmonic and sequence components measurement method based on modulated sliding discrete Fourier transform (mSDFT) and a variable sampling period technique. The proposal allows measuring the harmonic components of a three-phase signal and computes the corresponding imbalance by estimating the instantaneous symmetrical components. In addition, an adaptive variable sampling period is used to obtain a sampling frequency multiple of the main frequency. By doing so, DFT typical errors, known as spectral leakage and picket-fence effect, are mitigated in steady state. The proposal is tested with different disturbances by simulation and experimental results. Some results obtained with a power quality monitor implemented with the proposed system are also presented. The high rejection to distortion in the electrical network, frequency adaptability, flexibility, and good performance in power quality monitor application render the proposed method a promising alternative for signal processing from the mains.

Figure 1 is of the same form as Fig. 3 in Schrijvers et al. (1997): the upper part of each panel is the amplitude of the variation across the line at the mode frequency and the lower part is the phase shift of these two components across the line (in units of Φ). The parameters {Vavg, k, Ω/ω0, W} were chosen to have values representative of the δ Scuti star 4 CVn. Each panel in this array of plots has m=0, with a value of ∓ of 0, 1, or 2, and an inclination angle θi between 10° and 80°. In order to generate the synthetic line profiles, we use sampling times taken from the last week of the 1996 δ Scuti campaign on 4 CVn, and we assume that the signal-to-noise ratio of the spectrum is 250.

A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data

The RAVEN code has been under development at the Idaho National Laboratory since 2012. Its main goal is to create a multi-purpose platform for the deploying of all the capabilities needed for Probabilistic Risk Assessment, uncertainty quantification, data mining analysis and optimization studies. RAVEN is currently equipped with three different sampling categories: Forward samplers (Monte Carlo, Latin Hyper Cube, Stratified, Grid Sampler, Factorials, etc.), Adaptive Samplers (Limit Surface search, Adaptive Polynomial Chaos, etc.) and Dynamic Event Tree (DET) samplers (Deterministic and Adaptive Dynamic Event Trees). The main subject of this document is to report the activities that have been done in order to: start the migration of the RAVEN/RELAP-7 control logic system into MOOSE, and develop advanced dynamic sampling capabilities based on the Dynamic Event Tree approach. In order to provide to all MOOSE-based applications a control logic capability, in this Fiscal Year an initial migration activity has been initiated, moving the control logic system, designed for RELAP-7 by the RAVEN team, into the MOOSE framework. In this document, a brief explanation of what has been done is going to be reported. The second and most important subject of this report is about the development of a Dynamic Event Tree (DET) sampler named “Hybrid Dynamic Event Tree” (HDET) and its Adaptive variant “Adaptive Hybrid Dynamic Event Tree” (AHDET). As other authors have already reported, among the different types of uncertainties, it is possible to discern two principle types: aleatory and epistemic uncertainties. The classical Dynamic Event Tree is in charge of treating the first class (aleatory) uncertainties; the dependence of the probabilistic risk assessment and analysis on the epistemic uncertainties are treated by an initial Monte Carlo sampling (MCDET). From each Monte Carlo sample, a DET analysis is run (in total, N trees). The Monte Carlo employs a pre-sampling of the input space characterized by epistemic uncertainties. The consequent Dynamic Event Tree performs the exploration of the aleatory space. In the RAVEN code, a more general approach has been developed, not limiting the exploration of the epistemic space through a Monte Carlo method but using all the forward sampling strategies RAVEN currently employs. The user can combine a Latin Hyper Cube, Grid, Stratified and Monte Carlo sampling in order to explore the epistemic space, without any limitation. From this pre-sampling, the Dynamic Event Tree sampler starts its aleatory space exploration. As reported by the authors, the Dynamic Event Tree is a good fit to develop a goal-oriented sampling strategy. The DET is used to drive a Limit Surface search. The methodology that has been developed by the authors last year, performs a Limit Surface search in the aleatory space only. This report documents how this approach has been extended in order to consider the epistemic space interacting with the Hybrid Dynamic Event Tree methodology.

Repeated measures refer to multiple observations obtained in the same sampling plot or experimental unit. Such observations can be taken in a particular period and the same local space in many cases. In either case, repeated measures lead to correlated data. Statistical analysis using correlated data without an appropriate covariance structure would lead to Type I or Type II errors. This study used rainfall interception data from a coniferous forest in Mexico, May to September 2010, to develop a multi‐level linear model by assessing different covariance structures. Our main objectives were to evaluate the implications of these covariance structures in tests of fixed effects over categories of basal area and estimate differences between means and standard errors of each test. Based on the numerical inspection of the estimated correlations, their graphic representation, values of the statistics of fit (AICC and BIC) and considering that it is desirable to model a covariance structure in a parsimonious way, we concluded that the best selection for the structure of covariance was “heterogeneous Toeplitz.” Therefore, ‐values of fixed effects and the estimates of differences between means and standard errors of each test based on the “heterogeneous Toeplitz” covariance structure were considered the most appropriate among the analyzed covariance models.