Introduction to 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.

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.

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).

The study models non-Gaussian data analysis to identify risk factors associated with underweight among under-five children in rural Ethiopia.

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

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.

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.

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

INNC is non-parametric and, thus, is suitable for non-Gaussian data.

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

This algorithm can effectively process multivariate linear Gaussian, non-Gaussian and multivariate nonlinear non-Gaussian data.

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

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

Effect sizes were evaluated by Hedges’ g and Cliff’s δ for normal and non-Gaussian data, respectively.

Quantile regression is a powerful tool for modeling non-Gaussian data, and also for modeling different quantiles of the probability distributions of the responses.

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

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.

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.

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.

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.

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.

However two main challenges occur in this context: accounting for an informative survey design and handling non-Gaussian data types.

In recent researches, some distributions such as Beta distribution have demonstrated more flexibility in modeling asymmetric and non-Gaussian data.

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

The proposed approaches handle the non-Gaussian data based on categorizing and ranking.

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.

However, it is commonplace to encounter non-Gaussian data with small or medium sample sizes in practice.

More precisely, we present a new robust clustering algorithm designed for non-Gaussian data.

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.

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.