## What is/are Non Gaussian Data?

Non Gaussian Data - Data-driven machine learning methods, such as radial basis function network (RBFN), require minimal human intervention and provide effective alternatives for spatial interpolation of non-stationary and non-Gaussian data, particularly when measurements are sparse.^{[1]}For this, the relationships between the Environmental Performance Index (EPI), as the dependent variable, and the indicators of control of corruption, the effectiveness of an anti-monopoly policy, financial opportunities, undue influence, corporate culture, innovation output, GDP, and income growth among the poorest population, using a sample of 81 countries, and the technique for constructing nonlinear regression models based on the normalizing transformations for non-Gaussian data were studied.

^{[2]}The interpolation performance of the SLI method is investigated and compared with ordinary kriging using (i) synthetic non-Gaussian data and (ii) coal thickness measurements from approximately 11,500 drill holes (Campbell County, Wyoming, USA).

^{[3]}The study models non-Gaussian data analysis to identify risk factors associated with underweight among under-five children in rural Ethiopia.

^{[4]}Monte Carlo experiments show the estimation accuracy and computational efficiency of CAMM for modeling non-Gaussian data including fat-tailed and/or skewed distributions.

^{[5]}Naive Bayes classifiers were tested against non-Gaussian data, non-Gaussian feature weighted data, Gaussian-like data, and synthetically generated Gaussian data to observe the relationship between classifier performance and data distribution.

^{[6]}They have been effectively used in clustering non-Gaussian data and in Reproducibility Analysis, a meta-analysis method designed to verify the reliability and consistency of multiple high-throughput experiments.

^{[7]}We estimate the latent factors in high-dimensional panel non-Gaussian data using Higher-order multi-cumulant Factor Analysis (HFA).

^{[8]}INNC is non-parametric and, thus, is suitable for non-Gaussian data.

^{[9]}However, the well-known lack of robustness of PCA for non-Gaussian data and/or outliers often makes its practical use unreliable.

^{[10]}This algorithm can effectively process multivariate linear Gaussian, non-Gaussian and multivariate nonlinear non-Gaussian data.

^{[11]}In order to solve non-Gaussian data, LDA-based methods consider local structure information through measuring each pairwise distance of full connection graph.

^{[12]}Finally, a monitoring index based on support vector data description is constructed to eliminate adverse effects of non-Gaussian data for monitoring performance.

^{[13]}Effect sizes were evaluated by Hedges’ g and Cliff’s δ for normal and non-Gaussian data, respectively.

^{[14]}Quantile regression is a powerful tool for modeling non-Gaussian data, and also for modeling different quantiles of the probability distributions of the responses.

^{[15]}Our aim here is to reveal the structure of non-Gaussian data by generating new probabilistic SVM kernels from inverted-Beta Liouville mixture models.

^{[16]}The principle results of integrating geostatistics and machine learning indicate an improved estimation technique in domains with complex features, poorly defined domains, or non-Gaussian data.

^{[17]}This addresses the nonlinear and non-Gaussian data characteristics to support fault detection and prediction, within an explainable hybrid framework that captures causality in the complex engineered system.

^{[18]}Finally, we show that GAN is able to mimic PDF and number density of peaks for both Gaussian and non-Gaussian data with less than 0.

^{[19]}In the past, improvements of GAM estimation have focused on the smoothers used in the local scoring algorithm used for estimation, but poor prediction for non-Gaussian data motivates the need for robust estimation of GAMs.

^{[20]}Independent component analysis (ICA) is a recently developed method in which the goal is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible.

^{[21]}However two main challenges occur in this context: accounting for an informative survey design and handling non-Gaussian data types.

^{[22]}In recent researches, some distributions such as Beta distribution have demonstrated more flexibility in modeling asymmetric and non-Gaussian data.

^{[23]}Non-negative matrix factorization (NMF) is a new dimension reduction technique, which can effectively deal with Gaussian and non-Gaussian data.

^{[24]}This work applies recent developments in robust multivariate statistical methods to overcome issues with highly non-Gaussian data and support the development of a conceptual model for the regional groundwater chemistry and the occurrence of methane.

^{[25]}The study shows that data models have substantial impacts on Bayesian inference and predictive performance of the soil respiration models such that the following points are true: (i) the level of complexity of the best model is generally justified by the cross-validation results for different data models; (ii) not accounting for heteroscedasticity and autocorrelation might not necessarily result in biased parameter estimates or predictions, but will definitely underestimate uncertainty; (iii) using a non-Gaussian data model improves the parameter estimates and the predictive performance; and (iv) accounting for autocorrelation only or joint inversion of correlation and heteroscedasticity can be problematic and requires special treatment.

^{[26]}Traditional multivariate monitoring methods handle non-Gaussian data through combining both independent component analysis (ICA) and support vector data description (SVDD).

^{[27]}However, this is not sufficient to extract meaningful information in non-Gaussian data, which is the property of the process data in many industrial processes.

^{[28]}To model non-Gaussian data, a GP can be warped by a nonlinear transformation (or warping) as performed by warped GPs (WGPs) and more computationally-demanding alternatives such as Bayesian WGPs and deep GPs.

^{[29]}The model, confidence and prediction intervals of multiple non-linear regression for estimating the agile testing efforts for small Web projects are constructed on the basis of the Johnson multivariate normalizing transformation for non-Gaussian data with the help of appropriate techniques.

^{[30]}The traditional back propagation (BP) neural network requires a manual setting of a large number of parameters, and the extreme learning machine (ELM) algorithm simplifies the time complexity and does not need a manual setting of parameters, but the loss function in ELM based on second-order statistics is not the best solution when dealing with nonlinear and non-Gaussian data.

^{[31]}Since HOSA is a well suited technique for processing non-Gaussian data involving non-linear dynamics, good classification of thyroid texture can be obtained in US images as they also contain non-Gaussian Speckle noise and nonlinear characteristics.

^{[32]}In this paper, we propose an efficient and practical implementation of the ensemble Kalman filter based on trust region method for non-Gaussian data assimilation.

^{[33]}In this paper, we primarily focus on simultaneous testing mean vector and covariance matrix with high-dimensional non-Gaussian data, based on the classical likelihood ratio test.

^{[34]}Three aspects of the traditional Bayesian wavelet packet denoising method have been rarely discussed in the literature for mechanical signals: (1) how to reduce noise if a precise prior description is needed for non-Gaussian data; (2) how to programmatically select a reasonable decomposition level; and (3) how to evaluate the denoising effect from multiple factors.

^{[35]}First, it is illustrated that the concept of sparse finite mixture is very generic and easily extended to cluster various types of non-Gaussian data, in particular discrete data and continuous multivariate data arising from non-Gaussian clusters.

^{[36]}Gaussian data were analyzed using ANOVA and Bonferroni tests whereas non-Gaussian data were analyzed using Kruskal-Wallis and Dunn tests, considering significant p values less than 0.

^{[37]}TRNMDA does not have the assumption on data distribution that overcomes the limitation of LDA, which can not perform well in non-gaussian data.

^{[38]}Our model framework outperforms some existing state-of-art geostatistical modelling methods for simulated non-Gaussian data and is applied to a massive forestry dataset.

^{[39]}The proposed approaches handle the non-Gaussian data based on categorizing and ranking.

^{[40]}We also give a highly efficient algorithm, based on the alternating direction method of multipliers, for fitting the MQGM to high-dimensionaland potentially non-Gaussian data.

^{[41]}However, it is commonplace to encounter non-Gaussian data with small or medium sample sizes in practice.

^{[42]}More precisely, we present a new robust clustering algorithm designed for non-Gaussian data.

^{[43]}This paper presents a new mixture model that includes the inverted Beta mixture model (IBMM) as a special case to analyze the positive non-Gaussian data.

^{[44]}However, in practical scenarios, processes may have been corrupted by the outliers and other disturbances or have multiple modes of operation, resulting a non-Gaussian data likelihood.

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