A Polynomial Estimation of Measurand Parameters for Samples of Non-Gaussian Symmetrically Distributed Data

2014 ◽

Vol 10 (S306) ◽

pp. 258-261

Author(s):

Metin Ata ◽

Francisco-Shu Kitaura ◽

Volker Müller

Keyword(s):

Dark Matter ◽

Statistical Inference ◽

Computer Code ◽

Matter Density ◽

Density Field ◽

Distributed Data ◽

Dark Matter Density ◽

Posterior Sampling ◽

Non Linear ◽

Non Gaussian

AbstractWe study the statistical inference of the cosmological dark matter density field from non-Gaussian, non-linear and non-Poisson biased distributed tracers. We have implemented a Bayesian posterior sampling computer-code solving this problem and tested it with mock data based onN-body simulations.

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Polynomial estimation of the measurand parameters for samples from non-Gaussian distributions based on higher order statistics

Series on Advances in Mathematics for Applied Sciences - Advanced Mathematical and Computational Tools in Metrology and Testing XI ◽

10.1142/9789813274303_0039 ◽

2018 ◽

pp. 383-400 ◽

Cited By ~ 1

Author(s):

Zygmunt Lech Warsza ◽

Sergiej V. Zabolotnii

Keyword(s):

Order Statistics ◽

Higher Order ◽

Higher Order Statistics ◽

Gaussian Distributions ◽

Polynomial Estimation ◽

Non Gaussian

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An algorithm for arbitrary–order cumulant tensor calculation in a sliding window of data streams

International Journal of Applied Mathematics and Computer Science ◽

10.2478/amcs-2019-0015 ◽

2019 ◽

Vol 29 (1) ◽

pp. 195-206 ◽

Cited By ~ 3

Author(s):

Krzysztof Domino ◽

Piotr Gawron

Keyword(s):

Data Streams ◽

Data Stream ◽

Multivariate Data ◽

Sliding Window ◽

High Order ◽

Distributed Data ◽

Symmetric Tensors ◽

On Line ◽

Non Gaussian

Abstract High-order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of cumulants of arbitrary orders in a sliding window for data streams. We show that this algorithm offers substantial speedups of cumulant updates compared with the current solutions. The proposed algorithm can be used for processing on-line high-frequency multivariate data and can find applications, e.g., in on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an estimator of non-Gaussianity of a data stream based on the norms of high order cumulant tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a data stream. In order to achieve high implementation efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ a block structure to store and calculate only one hyper-pyramid part of such tensors.

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