Introduction to Non Gaussian Data

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. ^[45]