non-Gaussian Models Research Articles

Coupling Techniques for Nonlinear Ensemble Filtering

We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that harnesses transportation of measures, convex optimization, and ideas from probabilistic graphical models to yield robust ensemble approximations of the filtering distribution in high dimensions. Our approach can be understood as the natural generalization of the ensemble Kalman filter (EnKF) to nonlinear updates, using stochastic or deterministic couplings. The use of nonlinear updates can reduce the intrinsic bias of the EnKF at a marginal increase in computational cost. We avoid any form of importance sampling and introduce non-Gaussian localization approaches for dimension scalability. Our framework achieves state-of-the-art tracking performance on challenging configurations of the Lorenz-96 model in the chaotic regime.

Handbook of Regression Analysis with Applications in R (Second Edition)

The second edition of ‘Handbook of Regression Analysis with Applications in R’ motivated at providing a practical and comprehensive guide to practitioners of regression analysis using R programming language. The book has been divided into seven parts containing 16 chapters. The part I of the book consist of first 2 chapters discussing the basic concepts of linear regression model, model estimation, prediction and selection methodologies. Part II containing three chapters, 3–5, address the implications of violations of assumptions, analysis of leverage and outliers, robust regression techniques, estimation of linearisable non-linear models and models with auto-correlated disturbances. Part III of the book includes two chapters 6 and 7 on analysis of variance and analysis of covariance. Part IV covered in chapters 8–11 discuss various non-Gaussian regression models including Logistic and multinomial regression, count data model and survival models for time to event. The part V of the book consisting of chapters 12–14 demonstrates non-linear regression and non-linear least squares regression, longitudinal and nested data models, the sparsity in regression and regularisation methods of estimation. The last part VI covered in chapters 15 and 16 focusses on non-parametric and semi-parametric methods including smoothing and additive models and tree-based models such as CART.

Macrodispersion in generalized sub-Gaussian randomly heterogeneous porous media

• Features of log-conductivity, Y , fields are captured by a non-Gaussian (GSG) model. • Expressions of flow and transport moments in three-dimensional GSG fields are derived. • Head and velocity fields are more correlated in GSG than in Gaussian Y structures. • Non-Gaussianity of Y heavily influences pre-asymptotic macrodispersion values. • Late time transport exhibits a Fickian behavior also in non-Gaussian Y fields. In this work, we explore the implications of modeling the logarithm of hydraulic conductivity, Y , as a Generalized Sub-Gaussian (GSG) field on the features of conservative solute transport in randomly heterogeneous, three-dimensional porous media. Hydro-geological properties are often viewed as Gaussian random fields. Nevertheless, the GSG model enables us to capture documented non-Gaussian traits that are not explained through classical Gaussian models. Our formulation yields lead- (or first-) order analytical solutions for key statistical moments of flow and transport variables. These include flow velocities, hydraulic head, and macrodispersion coefficients, as obtained across GSG log-conductivity fields. The analytical model is based on a first-order spectral theory, which constrains the rigorous validity of our results to small values of log-conductivity variance ( σ Y 2 < < 1 ). Analytical results are then compared against detailed numerical estimates obtained through a Monte Carlo scheme encompassing various levels of domain heterogeneity. An asymptotic Fickian transport regime is attained at late times in both Gaussian and GSG Y fields. Convergence to such regime is slower for GSG as compared to Gaussian fields. This suggests a strong impact of the heterogeneity structure on non-Fickian pre-asymptotic behaviors of the kind documented in the literature. The quality of the comparison between analytical and numerical results deteriorates with increasing σ Y 2 . Otherwise, our lead-order solutions frame macrodispersion coefficients in appropriate orders of magnitude also for values of σ Y 2 up to approximately 1.7, which are consistent with the spatial variability of Y across a single geological unit. In this sense, our analytical approach enables one to obtain prior information on solute plume evolution and to grasp the effects of non-Gaussian medium heterogeneity while favoring simplicity. Our findings also enhance the current level of understanding of the nature of mass transfer across heterogeneous media characterized by complex variability structures which cannot be reconciled with classical Gaussian scenarios.

Revisiting spillovers between investor attention and cryptocurrency markets using noisy independent component analysis and transfer entropy

The present paper aims at revisiting the information transmission between cryptocurrency markets and investor attention in these assets. For this purpose, we use transfer entropy rather than the conventional Granger causality approach. The resort to transfer entropy is an interesting route to overcome the limitations of Granger’s concept of causality related to the linearity (and Gaussianity) assumption. In addition, a non-gaussian factor model is estimated to extract a proxy of investor attention from Google search volumes of a set of keywords. Whilst empirical studies commonly report a one-way causal effect between investor attention and price movements, our results shed light on a bidirectional spillover which can be attributed to the self-sustaining nature of price dynamics in speculative markets.

A new method for stochastic analysis of structures under limited observations

Reasonable modeling of non-Gaussian system inputs from limited observations and efficient propagation of system response are of great significance in uncertain analysis of real engineering problems. In this paper, we develop a new method for the construction of non-Gaussian random model and associated propagation of response under limited observations. Our method firstly develops a new kernel density estimation-based (KDE-based) random model based on Karhunen-Loeve (KL) expansion of observations of uncertain parameters. By further implementing the arbitrary polynomial chaos (aPC) formulation on KL vector with dependent measure, the associated aPC-based response propagation is then developed. In our method, the developed KDE-based model can accurately represent the input parameters from limited observations as the new KDE of KL vector can incorporate the inherent relation between marginals of input parameters and distribution of univariate KL variables. In addition, the aPC formulation can be effectively determined for uncertain analysis by virtue of the mixture representation of the developed KDE of KL vector. Furthermore, the system response can be propagated in a stable and accurate way with the developed D-optimal weighted regression method by the equivalence between the distribution of underlying aPC variables and that of KL vector. In this way, the current work provides an effective framework for the reasonable stochastic modeling and efficient response propagation of real-life engineering systems with limited observations. Two numerical examples, including the analysis of structures subjected to random seismic ground motion, are presented to highlight the effectiveness of the proposed method.

A welcome to the jungle of continuous-time multivariate non-Gaussian models based on Lévy processes applied to finance

A welcome to the jungle of continuous-time multivariate non-Gaussian models based on Lévy processes applied to finance

Impact of gut microbiome on dyslipidemia in japanese adults: Assessment of the Shika-machi super preventive health examination results for causal inference.

Dyslipidemia (DL) is one of the most common lifestyle-related diseases. There are few reports showing the causal relationship between gut microbiota (GM) and DL. In the present study, we used a linear non-Gaussian acyclic model (LiNGAM) to evaluate the causal relationship between GM and DL. A total of 79 men and 82 women aged 40 years or older living in Shika-machi, Ishikawa Prefecture, Japan were included in the analysis, and their clinical information was investigated. DNA extracted from the GM was processed to sequence the 16S rRNA gene using next-generation sequencing. Participants were divided into four groups based on sex and lipid profile information. The results of one-way analysis of covariance, linear discriminant analysis effect size, and least absolute value reduction and selection operator logistic regression model indicated that several bacteria between men and women may be associated with DL. The LiNGAM showed a presumed causal relationship between different bacteria and lipid profiles in men and women. In men, Prevotella 9 and Bacteroides were shown to be potentially associated with changes in low- and high-density lipoprotein cholesterol levels. In women, the LiNGAM results showed two bacteria, Akkermansia and Escherichia/Shigella, had a presumptive causal relationship with lipid profiles. These results may provide a new sex-based strategy to reduce the risk of developing DL and to treat DL through the regulation of the intestinal environment using specific GM.

WITHDRAWN: Risk-Return Trade-off in International Stock Returns: Skewness and Business Cycles

The fundamental risk-return relation is examined with a flexible regime switching model combining the impact of skewness and business cycle regimes in stock returns. Key methodological and empirical findings point out the need for a highly nonlinear and non-Gaussian model to get a reliable picture on the risk-return relationship. With an international dataset of major countries to global financial markets, the empirical results show that accounting especially for skewness patterns leads to the expected positive risk-return relation, which is importantly also maintained over different business cycle conditions.

A new mixture copula model for spatially correlated multiple variables with an environmental application

In environmental monitoring, multiple spatial variables are often sampled at a geographical location that can depend on each other in complex ways, such as non-linear and non-Gaussian spatial dependence. We propose a new mixture copula model that can capture those complex relationships of spatially correlated multiple variables and predict univariate variables while considering the multivariate spatial relationship. The proposed method is demonstrated using an environmental application and compared with three existing methods. Firstly, improvement in the prediction of individual variables by utilising multivariate spatial copula compares to the existing univariate pair copula method. Secondly, performance in prediction by utilising mixture copula in the multivariate spatial copula framework compares with an existing multivariate spatial copula model that uses a non-linear principal component analysis. Lastly, improvement in the prediction of individual variables by utilising the non-linear non-Gaussian multivariate spatial copula model compares to the linear Gaussian multivariate cokriging model. The results show that the proposed spatial mixture copula model outperforms the existing methods in the cross-validation of actual and predicted values at the sampled locations.

RBFNN for Calculating the Stationary Response of SDOF Nonlinear Systems Excited by Poisson White Noise

Random perturbations in nature described by non-Gaussian excitation models are far more widely applied and development prospects than that of Gaussian excitation models in practice. However, the stochastic dynamics research of non-Gaussian excitation is still not very mature. In this work, radial-basis-function-neural-network (RBFNN) is applied for calculating the stationary response of single-degree-of-freedom (SDOF) nonlinear system excited by Poisson white noise. Specifically, the trial probability-density-function (PDF) solution of reduced generalized-Fokker–Plank–Kolmogorov (GFPK) equation is constructed by a suitable number of Gaussian basis functions (GBFs) with a fixed set of means and standard deviations. Subsequently, an approximate squared error of the GFPK equation in a finite domain is considered. Together with the normalization condition, the approximate squared error can be minimized by establishing a Lagrangian function, and then the optimal weight coefficients associated with the approximate PDF solution are solved from a system of linear algebraic equations. For demonstrating the effectiveness of the proposed procedure, two specific examples are presented. The corresponding reduced GFPK equation is truncated with higher order for the strong non-Gaussian case. The precision of the analytical solution is verified against the Monte Carlo simulation (MCS) data. In addition, all the results indicate that RBFNN shows fairly high efficiency under the premise of ensuring high precision in the whole computational procedure.

Insights into Cation Ordering of Double Perovskite Oxides from Machine Learning and Causal Relations

This work investigates the origins of cation ordering of double perovskites using first-principles theory computations combined with machine learning (ML) and causal relations. We have considered various oxidation states of A, A', B, and B' from the family of transition metal ions to construct a diverse compositional space. A conventional framework employing traditional ML classification algorithms such as Random Forest (RF) coupled with appropriate features including geometry-driven and key structural modes leads to highly accurate prediction (~98%) of A-site cation ordering. We have evaluated the accuracy of ML models by entailing analyses of decision paths, assignments of probabilistic confidence bound, and finally introducing a direct non-Gaussian acyclic structural equation model to investigate causality. Our study suggests that the structural modes are the most important features for classifying layered, columnar and rock-salt ordering. For clear layered ordering, the charge difference between the A and A' is the most important feature which in turn depends on the B, B' charge separation. Based on the outputs from ML models, we have designed functional forms with these features to derive energy differences forming clear layered ordering. The trilinear coupling between tilt, rotation, and A-site antiferroelectric displacement in Landau free-energy expansion becomes the necessary condition behind the formation of A-site cation ordering.

A comparison study of monoexponential and fractional order calculus diffusion models and 18F-FDG PET in differentiating benign and malignant solitary pulmonary lesions and their pathological types.

ObjectiveTo evaluate the application value of monoexponential, fractional order calculus (FROC) diffusion models and PET imaging to distinguish between benign and malignant solitary pulmonary lesions (SPLs) and malignant SPLs with different pathological types and explore the correlation between each parameter and Ki67 expression.MethodsA total of 112 patients were enrolled in this study. Prior to treatment, all patients underwent a dedicated thoracic 18F-FDG PET/MR examination. Five parameters [including apparent diffusion coefficient (ADC) derived from the monoexponential model; diffusion coefficient (D), a microstructural quantity (μ), and fractional order parameter (β) derived from the FROC model and maximum standardized uptake value (SUVmax) derived from PET] were compared between benign and malignant SPLs and different pathological types of malignant SPLs. Independent sample t test, Mann-Whitney U test, DeLong test and receiver operating characteristic (ROC) curve analysis were used for statistical evaluation. Pearson correlation analysis was used to calculate the correlations between Ki-67 and ADC, D, μ, β, and SUVmax.ResultsThe ADC and D values were significantly higher and the μ and SUVmax values were significantly lower in the benign group [1.57 (1.37, 2.05) μm2/ms, 1.59 (1.52, 1.72) μm2/ms, 5.06 (3.76, 5.66) μm, 5.15 ± 2.60] than in the malignant group [1.32 (1.03, 1.51) μm2/ms, 1.43 (1.29, 1.52) μm2/ms, 7.06 (5.87, 9.45) μm, 9.85 ± 4.95]. The ADC, D and β values were significantly lower and the μ and SUVmax values were significantly higher in the squamous cell carcinoma (SCC) group [1.29 (0.66, 1.42) μm2/ms, 1.32 (1.02, 1.42) μm2/ms, 0.63 ± 0.10, 9.40 (7.76, 15.38) μm, 11.70 ± 5.98] than in the adenocarcinoma (AC) group [1.40 (1.28, 1.67) μm2/ms, 1.52 (1.44, 1.64) μm2/ms, 0.70 ± 0.10, 5.99 (4.54, 6.87) μm, 8.76 ± 4.18]. ROC curve analysis showed that for a single parameter, μ exhibited the best AUC value in discriminating between benign and malignant SPLs groups and AC and SCC groups (AUC = 0.824 and 0.911, respectively). Importantly, the combination of monoexponential, FROC models and PET imaging can further improve diagnostic performance (AUC = 0.872 and 0.922, respectively). The Pearson correlation analysis showed that Ki67 was positively correlated with μ value and negatively correlated with ADC and D values (r = 0.402, -0.346, -0.450, respectively).ConclusionThe parameters D and μ derived from the FROC model were superior to ADC and SUVmax in distinguishing benign from malignant SPLs and adenocarcinoma from squamous cell carcinoma, in addition, the combination of multiple parameters can further improve diagnostic performance. The non-Gaussian FROC diffusion model is expected to become a noninvasive quantitative imaging technique for identifying SPLs.

Causal Discovery in Linear Non-Gaussian Acyclic Model With Multiple Latent Confounders.

Causal discovery from observational data is a fundamental problem in science. Though the linear non-Gaussian acyclic model (LiNGAM) has shown promising results in various applications, it still faces the following challenges in the data with multiple latent confounders: 1) how to detect the latent confounders and 2) how to uncover the causal relations among observed and latent variables. To address these two challenges, we propose a hybrid causal discovery method for the LiNGAM with multiple latent confounders (MLCLiNGAM). First, we utilize the constraint-based method to learn the causal skeleton. Second, we identify the causal directions, by conducting regression and independence tests on the adjacent pairs in the causal skeleton. Third, we detect the latent confounders with the help of the maximal clique patterns raised by the latent confounders and reconstruct the causal structure with latent variables. Theoretical results show the correctness and efficiency of the algorithms. We conduct extensive experiments on synthetic and real data, which illustrates the efficiency and effectiveness of the proposed algorithms.

Elucidation of the mechanism of cognitive decline in mild cognitive impairment using causal discovery

Mild cognitive impairment (MCI) is the stage between the expected cognitive decline of normal aging and the more serious decline of dementia. Since MCI may increase risk of later developing dementia caused by Alzheimer's disease (AD) or other neurological conditions, it is important to detect and treat MCI early in order to prevent dementia. Causal discovery, which can visualize causal relationships (cause and effect) among data, has recently been attracting attention. One of its algorithms, the Linear Non-Gaussian Acyclic Model (LiNGAM), can extract causal relationships among variables from statistical data only, using probability distributions of variables that are generally non-Gaussian. In this study, we used LiNGAM to analyze gene expression data in the hippocampus of healthy subjects and of MCI patients, and also the Mini-Mental State Examination (MMSE) scores, which are used to assess cognitive decline. We found that cell adhesion molecule 4 (CADM4) gene regulates cognitive processes that are measured in terms of MMSE scores. Our results revealed a causal relationship between gene expression changes and MMSE scores, and allowed us to identify the genes responsible for cognitive decline..

Residual Similarity Based Conditional Independence Test and Its Application in Causal Discovery

Recently, many regression based conditional independence (CI) test methods have been proposed to solve the problem of causal discovery. These methods provide alternatives to test CI by first removing the information of the controlling set from the two target variables, and then testing the independence between the corresponding residuals Res1 and Res2. When the residuals are linearly uncorrelated, the independence test between them is nontrivial. With the ability to calculate inner product in high-dimensional space, kernel-based methods are usually used to achieve this goal, but still consume considerable time. In this paper, we investigate the independence between two linear combinations under linear non-Gaussian structural equation model. We show that the dependence between the two residuals can be captured by the difference between the similarity of (Res1, Res2) and that of (Res1, Res3) (Res3 is generated by random permutation) in high-dimensional space. With this result, we design a new method called SCIT for CI test, where permutation test is performed to control Type I error rate. The proposed method is simpler yet more efficient and effective than the existing ones. When applied to causal discovery, the proposed method outperforms the counterparts in terms of both speed and Type II error rate, especially in the case of small sample size, which is validated by our extensive experiments on various datasets.

Non-Gaussian stochastic dynamical model for the El Niño southern oscillation

Non-Gaussian stochastic dynamical model for the El Niño southern oscillation

Application of Continuous Non-Gaussian Mortality Models with Markov Switchings to Forecast Mortality Rates

The ongoing pandemic has resulted in the development of models dealing with the rate of virus spread and the modelling of mortality rates μx,t. A new method of modelling the mortality rates μx,t with different time intervals of higher and lower dispersion has been proposed. The modelling was based on the Milevski–Promislov class of stochastic mortality models with Markov switches, in which excitations are modelled by second-order polynomials of results from a linear non-Gaussian filter. In contrast to literature models where switches are deterministic, the Markov switches are proposed in this approach, which seems to be a new idea. The obtained results confirm that in the time intervals with a higher dispersion of μx,t, the proposed method approximates the empirical data more accurately than the commonly used the Lee–Carter model.

A Generic Formula and Some Special Cases for the Kullback-Leibler Divergence between Central Multivariate Cauchy Distributions.

This paper introduces a closed-form expression for the Kullback–Leibler divergence (KLD) between two central multivariate Cauchy distributions (MCDs) which have been recently used in different signal and image processing applications where non-Gaussian models are needed. In this overview, the MCDs are surveyed and some new results and properties are derived and discussed for the KLD. In addition, the KLD for MCDs is showed to be written as a function of Lauricella D-hypergeometric series . Finally, a comparison is made between the Monte Carlo sampling method to approximate the KLD and the numerical value of the closed-form expression of the latter. The approximation of the KLD by Monte Carlo sampling method are shown to converge to its theoretical value when the number of samples goes to the infinity.

SPSA Algorithm for Matching of Historical Data for Complex Non-Gaussian Geological Models

History matching is the process of integrating dynamic production data in the reservoir model. It consists in estimation of uncertain model parameters such that oil or water production data from flow simulation become close to observed dynamic data. Various optimization methods can be used to estimate the model parameters. Simultaneous perturbation stochastic approximation (SPSA) is one of the stochastic approximation algorithms. It requires only two objective function measurements for gradient approximation per iteration. Also parameters estimated by this algorithm might converge to their true values under arbitrary bounded additive noise, while many other optimization algorithms require the noise to have zero mean. SPSA algorithm has not been well explored for history matching problems and has been applied only to simple Gaussian models. In this paper, we applied SPSA to history matching of binary channelized reservoir models. We also used SPSA in combination with parameterization method CNN-PCA. And we considered the case of complex noise in observed production data and with objective function that does not require assumptions of normality of the observations, which is common in history matching literature. We experimentally showed that SPSA method can be successfully used for history matching of non-Gaussian geological models with different types of noise in observations and outperforms Particle Swarm Optimization by convergence speed.

Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers

Directed acyclic graph (DAG) models are widely used to represent casual relationships among random variables in many application domains. This article studies a special class of non-Gaussian DAG models, where the conditional variance of each node given its parents is a quadratic function of its conditional mean. Such a class of non-Gaussian DAG models are fairly flexible and admit many popular distributions as special cases, including Poisson, Binomial, Geometric, Exponential, and Gamma. To facilitate learning, we introduce a novel concept of topological layers, and develop an efficient DAG learning algorithm. It first reconstructs the topological layers in a hierarchical fashion and then recovers the directed edges between nodes in different layers, which requires much less computational cost than most existing algorithms in literature. Its advantage is also demonstrated in a number of simulated examples, as well as its applications to two real-life datasets, including an NBA player statistics data and a cosmetic sales data collected by Alibaba. Supplementary materials for this article are available online.