On irregular sampling in Bernstein spaces

2015 ◽  
Vol 353 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Alexander Olevskii ◽  
Alexander Ulanovskii
Keyword(s):  
Irregular Sampling ◽  
Bernstein Spaces

On Irregular Sampling and Interpolation in Bernstein Spaces

2018 ◽  
Vol 303 (1) ◽  
pp. 178-192
Author(s):  
Alexander Olevskii ◽  
Alexander Ulanovskii
Keyword(s):  
Irregular Sampling ◽  
Bernstein Spaces

scholarly journals Bias correction for direct spectral estimation from irregularly sampled data including sampling schemes with correlation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nils Damaschke ◽  
Volker Kühn ◽  
Holger Nobach
Keyword(s):  
Spectral Estimation ◽  
Continuous Distribution ◽  
Discrete Distribution ◽  
Irregular Sampling ◽  
The Other ◽  
Sampled Data ◽  
Sampling Schemes ◽  
Other Hand ◽  
Sampling Intervals ◽  
Irregularly Sampled Data

AbstractThe prediction and correction of systematic errors in direct spectral estimation from irregularly sampled data taken from a stochastic process is investigated. Different sampling schemes are investigated, which lead to such an irregular sampling of the observed process. Both kinds of sampling schemes are considered, stochastic sampling with non-equidistant sampling intervals from a continuous distribution and, on the other hand, nominally equidistant sampling with missing individual samples yielding a discrete distribution of sampling intervals. For both distributions of sampling intervals, continuous and discrete, different sampling rules are investigated. On the one hand, purely random and independent sampling times are considered. This is given only in those cases, where the occurrence of one sample at a certain time has no influence on other samples in the sequence. This excludes any preferred delay intervals or external selection processes, which introduce correlations between the sampling instances. On the other hand, sampling schemes with interdependency and thus correlation between the individual sampling instances are investigated. This is given whenever the occurrence of one sample in any way influences further sampling instances, e.g., any recovery times after one instance, any preferences of sampling intervals including, e.g., sampling jitter or any external source with correlation influencing the validity of samples. A bias-free estimation of the spectral content of the observed random process from such irregularly sampled data is the goal of this investigation.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

scholarly journals Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

2018 ◽  
Vol 22 (2) ◽  
pp. 1175-1192 ◽  
Author(s):  
Qian Zhang ◽  
Ciaran J. Harman ◽  
James W. Kirchner
Keyword(s):  
Water Quality ◽  
Time Series ◽  
Irregular Sampling ◽  
Quality Data ◽  
Sampled Data ◽  
Spectral Slope ◽  
Water Quality Data ◽  
Fractal Scaling ◽  
Wide Range ◽  
Irregularly Sampled Data

Abstract. River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β  =  0) to Brown noise (β  =  2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

Synthetic Data Generation to Support Irregular Sampling in Sensor Networks

2004 ◽  
pp. 211-234 ◽  
Author(s):  
Lewis Girod ◽  
Ramesh Govindan ◽  
Deepak Ganesan ◽  
Deborah Estrin ◽  
Yan Yu
Keyword(s):  
Sensor Networks ◽  
Synthetic Data ◽  
Irregular Sampling ◽  
Data Generation ◽  
Synthetic Data Generation

scholarly journals COMPORTAMENTO ESPACIAL DA FUSARIOSE E DOS ATRIBUTOS DO SOLO NO CULTIVO DA PIMENTA-DO-REINO

Nativa ◽  
2018 ◽  
Vol 6 (2) ◽  
pp. 113
Author(s):  
Carla Da Penha Simon ◽  
Ana Carolina Lyra Brumat ◽  
Marcelo Barreto Da Silva ◽  
Bernardo Torres Olmo ◽  
Edney Leandro da Vitória ◽  
...  
Keyword(s):  
Organic Matter ◽  
Soil Texture ◽  
Fusarium Solani ◽  
Nutrient Content ◽  
Black Pepper ◽  
Irregular Sampling ◽  
Piper Nigrum ◽  
Soil Attributes ◽  
Calcium Magnesium ◽  
Chemical Attributes

A pimenta-do-reino é a especiaria mais consumida no mundo e o Brasil destaca-se como um dos maiores produtores. Um dos grandes limitantes no seu cultivo é a fusariose (Fusarium solani f. sp. piperis). Objetivou-se com a realização deste estudo caracterizar a variabilidade espacial da fusariose em pimenta-do-reino, verificando a existência de relação com os atributos físicos e químicos do solo. O estudo foi desenvolvido em uma lavoura localizada no município de São Mateus-ES, na qual foi estabelecida uma malha amostral irregular com 79 pontos, abrangendo uma área de um hectare.  Para a amostragem da fusariose foi realizado um levantamento, onde uma planta por ponto da malha amostral foi classificada em sadia, doente ou morta.  Os atributos do solo amostrados foram: pH em H2O, matéria orgânica, cálcio, magnésio, potássio e textura do solo. Os dados foram analisados através da estatística descritiva e ferramentas da geoestatística. Os semivariogramas ajustados apresentaram uma forte dependência espacial para as variáveis intensidade da fusariose, altimetria, matéria orgânica, textura do solo, pH, cálcio, magnésio potássio (89, 94, 92, 94, 93, 91, 100 e 85 % respectivamente). Os mapas gerados indicam que não há relação da intensidade da fusariose com os atributos do solo estudados no experimento.Palavra-chave: epidemiologia, Fusarium solani f. sp. piperis, geoestatística, Piper nigrum L. SPATIAL ANALYSIS OF FUSARIOSE AND SOIL ATTRIBUTES IN THE BLACK PEPPER CULTIVATION  ABSTRACT:Black pepper is the most consumed spice in the world, Brazil stands out as one of the largest producers. One of the major constraints in cultivation is fusariosis (Fusarium solani f. Piperis). The objective of this study was characterize the spatial variability of fusariosis in black pepper and verify the relationship of chemical attributes of the soil. The study was developed in a tillage located in the municipality of São Mateus - ES, which exist an irregular sampling network was established with 79 points, covering an area of one hectare. For the sampling of fusariosis intensity, the survey was performed, where one plant per point of the sample mesh was classified as healthy, symptomatic or dead. The attributes of the soil sampled were: pH in H2O, organic matter, nutrient content (calcium, magnesium, potassium) and soil texture. Data were analyzed through descriptive statistics and geostatistics tools. The adjusted semivariograms indicated a strong spatial dependence for the variables intensity of fusariosis, altimetry, organic matter, soil texture, pH, calcium, potassium magnesium (89, 94, 92, 94, 93, 91, 100 and 85%, respectively). The generated maps indicate that there is no relation between the incidence of fusariosis and the soil attributes studied in the experiment.Keywords: epidemiology, Fusarium solani f. sp. piperis, geostatistics, Piper nigrum L. DOI:

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