Mixture Of Normal Distributions Research Articles

Integrated deviance information criterion for spatial autoregressive models with heteroskedasticity

In this study, we introduce the integrated deviance information criterion (DIC) for nested and non-nested model selection problems in heteroskedastic spatial autoregressive models. In a Bayesian estimation setting, we assume that the idiosyncratic error terms of our spatial autoregressive model have a scale mixture of normal distributions, where the scale mixture variables are latent variables that induce heteroskedasticity. We first derive the integrated likelihood function by analytically integrating out the scale mixture variables from the complete-data likelihood function. We then use the integrated likelihood function to formulate the integrated DIC measure. We investigate the finite sample performance of the integrated DIC in selecting the true model in a simulation study. The simulation results show that the integrated DIC performs satisfactorily and can be useful for selecting the correct model in specification search exercises. Finally, in a spatially augmented economic growth model, we use the integrated DIC to choose the spatial weights matrix that leads to better predictive accuracy.

Predictive Model for EV Charging Load Incorporating Multimodal Travel Behavior and Microscopic Traffic Simulation

A predictive model for the spatiotemporal distribution of electric vehicle (EV) charging load is proposed in this paper, considering multimodal travel behavior and microscopic traffic simulation. Firstly, the characteristic variables of travel time are fitted using advanced techniques such as Gaussian mixture distribution. Simultaneously, the user’s multimodal travel behavior is delineated by introducing travel purpose transfer probabilities, thus establishing a comprehensive travel spatiotemporal model. Secondly, the improved Floyd algorithm is employed to select the optimal path, taking into account various factors including signal light status, vehicle speed, and the position of starting and ending sections. Moreover, the approach of multi-lane lane change following and the utilization of cellular automata theory are introduced. To establish a microscopic traffic simulation model, a real-time energy consumption model is integrated with the aforementioned techniques. Thirdly, the minimum regret value is leveraged in conjunction with various other factors, including driving purpose, charging station electricity price, parking cost, and more, to simulate the decision-making process of users regarding charging stations. Subsequently, an EV charging load predictive framework is proposed based on the approach driven by electricity prices and real-time interaction of coupled network information. Finally, this paper conducts large-scale simulations to analyze the spatiotemporal distribution characteristics of EV charging load using a regional transportation network in East China and a typical power distribution network as case studies, thereby validating the feasibility of the proposed method.

Type I Tobit Bayesian Additive Regression Trees for censored outcome regression

Censoring occurs when an outcome is unobserved beyond some threshold value. Methods that do not account for censoring produce biased predictions of the unobserved outcome. This paper introduces Type I Tobit Bayesian Additive Regression Tree (TOBART-1) models for censored outcomes. Simulation results and real data applications demonstrate that TOBART-1 produces accurate predictions of censored outcomes. TOBART-1 provides posterior intervals for the conditional expectation and other quantities of interest. The error term distribution can have a large impact on the expectation of the censored outcome. Therefore, the error is flexibly modeled as a Dirichlet process mixture of normal distributions. An R package is available at https://github.com/EoghanONeill/TobitBART.

A replica exchange preconditioned Crank-Nicolson Langevin dynamic MCMC method with multi-variance strategy for Bayesian inverse problems

The preconditioned Crank-Nicolson Markov Chain Monte Carlo (pCN-MCMC) method is an efficient approach for large-scale Bayesian inference problems. It is constructed by discretizing a stochastic partial differential equation (SPDE). When the gradient information is coupled in this SPDE, the corresponding SPDE is also referred to as the Langevin diffusion. In this work, we present the replica exchange preconditioned Crank-Nicolson Langevin dynamic (repCNLD) Monte Carlo method to speed up the convergence of the pCN-MCMC and tackle the challenge of multimodal distribution. We use the Crank-Nicolson scheme to discretize the repLD and set the preconditioned matrix as the covariance matrix of the Gaussian prior. The discretization error is analyzed. Moreover, we use the multi-variance strategy (m-repCNLD) to improve computational efficiency. Perturbations are introduced into the scheme due to the likelihood estimation error, leading to the biased swapping rate. To correct the bias, we provide an unbiased estimator derived from some assumptions on the forward solvers. The accuracy and efficiency of the proposed method are demonstrated by sampling Gaussian mixture distribution and solving PDE-based nonlinear inverse problems numerically.

Skew Multiple Scaled Mixtures of Normal Distributions with Flexible Tail Behavior and Their Application to Clustering

Skew Multiple Scaled Mixtures of Normal Distributions with Flexible Tail Behavior and Their Application to Clustering

Inference of genomic landscapes using ordered Hidden Markov Models with emission densities (oHMMed).

Genomes are inherently inhomogeneous, with features such as base composition, recombination, gene density, and gene expression varying along chromosomes. Evolutionary, biological, and biomedical analyses aim to quantify this variation, account for it during inference procedures, and ultimately determine the causal processes behind it. Since sequential observations along chromosomes are not independent, it is unsurprising that autocorrelation patterns have been observed e.g., in human base composition. In this article, we develop a class of Hidden Markov Models (HMMs) called oHMMed (ordered HMM with emission densities, the corresponding R package of the same name is available on CRAN): They identify the number of comparably homogeneous regions within autocorrelated observed sequences. These are modelled as discrete hidden states; the observed data points are realisations of continuous probability distributions with state-specific means that enable ordering of these distributions. The observed sequence is labelled according to the hidden states, permitting only neighbouring states that are also neighbours within the ordering of their associated distributions. The parameters that characterise these state-specific distributions are inferred. We apply our oHMMed algorithms to the proportion of G and C bases (modelled as a mixture of normal distributions) and the number of genes (modelled as a mixture of poisson-gamma distributions) in windows along the human, mouse, and fruit fly genomes. This results in a partitioning of the genomes into regions by statistically distinguishable averages of these features, and in a characterisation of their continuous patterns of variation. In regard to the genomic G and C proportion, this latter result distinguishes oHMMed from segmentation algorithms based in isochore or compositional domain theory. We further use oHMMed to conduct a detailed analysis of variation of chromatin accessibility (ATAC-seq) and epigenetic markers H3K27ac and H3K27me3 (modelled as a mixture of poisson-gamma distributions) along the human chromosome 1 and their correlations. Our algorithms provide a biologically assumptionfree approach to characterising genomic landscapes shaped by continuous, autocorrelated patterns of variation. Despite this, the resulting genome segmentation enables extraction of compositionally distinct regions for further downstream analyses.

Capturing Valuation Study Sampling Uncertainty in the Estimation of Health State Utility Values Using the EQ-5D-3L.

Utility scores associated with preference-based health-related quality-of-life instruments such as the EQ-5D-3L are reported as point estimates. In this study, we develop methods for capturing the uncertainty associated with the valuation study of the UK EQ-5D-3L that arises from the variability inherent in the underlying data, which is tacitly ignored by point estimates. We derive a new tariff that properly accounts for this and assigns a specific closed-form distribution to the utility of each of the 243 health states of the EQ-5D-3L. Using the UK EQ-5D-3L valuation study, we used a Bayesian approach to obtain the posterior distributions of the derived utility scores. We constructed a hierarchical model that accounts for model misspecification and the responses of the survey participants to obtain Markov chain Monte Carlo (MCMC) samples from the posteriors. The posterior distributions were approximated by mixtures of normal distributions under the Kullback-Leibler (KL) divergence as the criterion for the assessment of the approximation. We considered the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to estimate the parameters of the mixture distributions. We derived an MCMC sample of total size 4,000 × 243. No evidence of nonconvergence was found. Our model was robust to changes in priors and starting values. The posterior utility distributions of the EQ-5D-3L states were summarized as 3-component mixtures of normal distributions, and the corresponding KL divergence values were low. Our method accounts for layers of uncertainty in valuation studies, which are otherwise ignored. Our techniques can be applied to other instruments and countries' populations. Guidelines for health technology assessments typically require that uncertainty be accounted for in economic evaluations, but the parameter uncertainty of the regression model used in the valuation study of the health instrument is often tacitly ignored.We consider the UK valuation study of the EQ-5D-3L and construct a Bayesian model that accounts for layers of uncertainty that would otherwise be disregarded, and we derive closed-form utility distributions.The derived tariff can be used by researchers in economic evaluations, as it allows analysts to directly sample a utility value from its corresponding distribution, which reflects the associated uncertainty of the utility score.

Tolerance Interval for the Mixture Normal Distribution Based on Generalized Extreme Value Theory

For a common type of mixture distribution, namely the mixture normal distribution, existing methods for constructing its tolerance interval are unsatisfactory for cases of small sample size and large content. In this study, we propose a method to construct a tolerance interval for the mixture normal distribution based on the generalized extreme value theory. The proposed method is implemented on simulated as well as real-life datasets and its performance is compared with the existing methods.

Multivariate Functional Clustering with Variable Selection and Application to Sensor Data from Engineering Systems

Multisensor data that track system operating behaviors are widely available nowadays from various engineering systems. Measurements from each sensor over time form a curve and can be viewed as functional data. Clustering of these multivariate functional curves is important for studying the operating patterns of systems. One complication in such applications is the possible presence of sensors whose data do not contain relevant information. Hence, it is desirable for the clustering method to equip with an automatic sensor selection procedure. Motivated by a real engineering application, we propose a functional data clustering method that simultaneously removes noninformative sensors and groups functional curves into clusters using informative sensors. Functional principal component analysis is used to transform multivariate functional data into a coefficient matrix for data reduction. We then model the transformed data by a Gaussian mixture distribution to perform model-based clustering with variable selection. Three types of penalties, the individual, variable, and group penalties, are considered to achieve automatic variable selection. Extensive simulations are conducted to assess the clustering and variable selection performance of the proposed methods. The application of the proposed methods to an engineering system with multiple sensors shows the promise of the methods and reveals interesting patterns in the sensor data. History: Kwok Tsui served as the senior editor for this article. Funding: The research by J. Min and Y. Hong was partially supported by the National Science Foundation [Grant CMMI-1904165] to Virginia Tech. The work by Y. Hong was partially supported by the Virginia Tech College of Science Research Equipment Fund. Data Ethics & Reproducibility Note: The original dataset is proprietary and cannot be shared. The full code to replicate the results in this paper, based on summary statistics of the original data, is available at https://github.com/jiem3/MultiFuncClustering . The code applied to a simplified version is available at https://codeocean.com/capsule/4041000/tree/v1 , which covers the data analysis and part of the simulation scenarios with a single dataset under each scenario using a fixed set of hyperparameters, for reducing computation time, and at https://doi.org/10.1287/ijds.2022.0034 .

New Classes of the Greedy-Applicable Arm Feature Distributions in the Sparse Linear Bandit Problem

We consider the sparse contextual bandit problem where arm feature affects reward through the inner product of sparse parameters. Recent studies have developed sparsity-agnostic algorithms based on the greedy arm selection policy. However, the analysis of these algorithms requires strong assumptions on the arm feature distribution to ensure that the greedily selected samples are sufficiently diverse; One of the most common assumptions, relaxed symmetry, imposes approximate origin-symmetry on the distribution, which cannot allow distributions that has origin-asymmetric support. In this paper, we show that the greedy algorithm is applicable to a wider range of the arm feature distributions from two aspects. Firstly, we show that a mixture distribution that has a greedy-applicable component is also greedy-applicable. Second, we propose new distribution classes, related to Gaussian mixture, discrete, and radial distribution, for which the sample diversity is guaranteed. The proposed classes can describe distributions with origin-asymmetric support and, in conjunction with the first claim, provide theoretical guarantees of the greedy policy for a very wide range of the arm feature distributions.

DiffGAN: An adversarial diffusion model with local transformer for MRI reconstruction

Magnetic resonance imaging (MRI) is non-invasive and crucial for clinical diagnosis, but it has long acquisition time and aliasing artifacts. Accelerated imaging techniques can effectively reduce the scanning time of MRI, thereby decreasing the anxiety and discomfort of patients. Vision Transformer (ViT) based methods have greatly improved MRI image reconstruction, but their computational complexity and memory requirements for the self-attention mechanism grow quadratically with image resolution, which limits their use for high resolution images. In addition, the current generative adversarial networks in MRI reconstruction are difficult to train stably. To address these problems, we propose a Local Vision Transformer (LVT) based adversarial Diffusion model (Diff-GAN) for accelerating MRI reconstruction. We employ a generative adversarial network (GAN) as the reverse diffusion model to enable large diffusion steps. In the forward diffusion module, we use a diffusion process to generate Gaussian mixture distribution noise, which mitigates the gradient vanishing issue in GAN training. This network leverages the LVT module with the local self-attention, which can capture high-quality local features and detailed information. We evaluate our method on four datasets: IXI, MICCAI 2013, MRNet and FastMRI, and demonstrate that Diff-GAN can outperform several state-of-the-art GAN-based methods for MRI reconstruction.

Regression with continuous mixture of Gaussian distributions for modeling the memory time of water treatment

. In this article, a new model of regression with a continuous mixture of Gaussian distributions is developed. The proposed model is applied for the prediction of the time memory of water treatment corresponding to the minimal conductivity. The model training is performed on the basis of a dataset concerning the conductivity of the water and its variations. In order to estimate the regression parameters, we suggested an extension of the expectation maximization (EM) algorithm. More precisely, we explicitly computed the conditional expectation of the complete data log-likelihood in the EM algorithm. The results of this algorithm provide consistent estimators of the parameters. The calibrated regression model with a continuous mixture of Gaussian distributions outperforms the classical regression model, as shown in the numerical analysis. We prove that the EM algorithm outperforms the two-Stage Least Squares method. These results are presented to illustrate the performance and applicability of this proposed model in water treatment.

Optimal dichotomization of bimodal Gaussian mixtures

AbstractDespite criticism for loss of information and power, dichotomization of variables is still frequently used in social, behavioral, and medical sciences, mainly because it yields more interpretable conclusions for research outcomes and is useful for decision making. However, the artificial choice of cut-points can be controversial and needs proper justification. In this work, we investigate the properties of point-biserial correlation after dichotomization with underlying bimodal Gaussian mixture distributions. We propose a dichotomous grouping procedure that considers the largest standardized difference in group mean while minimizing information loss.

OTFS Detection Based on Gaussian Mixture Distribution: A Generalized Message Passing Approach

OTFS Detection Based on Gaussian Mixture Distribution: A Generalized Message Passing Approach

Dimension reduction for constructing high-dimensional response distributions by accounting for unimportant and important variables

Probability distributions of responses have been widely used in structural analysis and design because of their complete statistical information. In practice, the dimensionality of input variables could easily reach hundreds or thousands, making it computationally expensive to obtain accurate distributions. In this paper, a generalized most probable point (MPP) method is developed to effectively build the response distributions of high-dimensional problems. First, a global index based on one-iteration MPPs is presented for dimension reduction, which is to divide the input variables into important and unimportant variables. After fixing the unimportant variables at their one-iteration MPP components, the MPP components of the important variables are obtained by performing the inverse first-order reliability method (FORM) in the reduced space. Predictive models of the all MPP components are then established to quickly estimate the MPPs of other cumulative distribution function (CDF) values. To accurately calculate CDF points of limit state functions with different shapes, a comprehensive uncertainty analysis method that accommodates the contributions of the important and unimportant variables is proposed by multiple combinations of FORM, second-order reliability method, and second-order saddlepoint approximation. Finally, the response distributions are generated based on Gaussian mixture distribution and all CDF points. The effectiveness of the proposed method is verified by a mathematical example and two engineering cases.

Generalized asymmetric mixture normal distribution: properties and applications

A new class of skew generalized normal distribution as a generalization of the skew-normal distribution of Arellano-Valle (Commun. Statist. Theor. Meth., 2004) and Kumar and Anusree (Commun. Statist. Theor. Meth., 2015) are considered. Several statistical properties of the proposed class of distributions are investigated and the location-scale extension of the model is obtained. Further, the estimation of its parameters by the method of maximum likelihood estimation is discussed and the distribution has been fitted to specific real-life data sets to illustrate the model’s usefulness. In addition, a brief simulation study is conducted for examining the performance of likelihood estimators of the parameters of the proposed model.

Tensile behaviour of pitting corroded steel bars: Laboratory investigation and probabilistic-based analysis

Localised corrosion in steel bars has been a long-standing issue in the durability of reinforced concrete structures, but a comprehensive scheme for the analysis of pitting corroded steel bars, especially with respect to the deformation capacity, is not currently available. In this study, the morphological characteristics of 27 pitting steel bars were captured using a 3D scanner. The measured data were used to establish the probability distribution model of the cross-sectional areas of the corroded bars. Uniaxial tensile tests were conducted, and the evolving deformation field of the corroded bars was recorded through Digital Image Correlation (DIC). Based on the 3D reconstructed model and DIC results, an analytical method for evaluating the mechanical properties of pitting steel bars was developed and validated. The results show that the two-component Gaussian mixture distribution model outperforms conventional unimodal distribution models. Comparison of the analytical results with experimental data demonstrates that the proposed procedure is capable of predicting not only the ultimate strength but also the gauge length-dependent ultimate strain of corroded bars. Additionally, there exists a strengthening effect in the ultimate stress at the critical sections and this effect should not be ignored for accurate predictions.

Defect detection enhancement using Gaussian Sparse Models

Detecting defects is critical in industrial fabrication, such as pipe welding, where radiography testing (RT) is the gold standard as a non-destructive method for monitoring weld quality and weld corrosion. The extraction of seamless information from radiographic images is critical for this approach. Image processing techniques can improve the quality of radiographic images by enhancing image contrast, especially in flawed regions. In this study, a method based on Gaussian mixture models was implemented and applied to radiographs of welded objects to improve visualization and detectability. In the Sparse Coding and Gaussian Scale Mixture method (SSC-GSM), the local image patches are described as a mixture of Gaussian distributions. Given the different levels of noise in the individual images, the background was determined and subtracted from each original image. The results show that the proposed techniques can maintain and improve the edge information in radiographs and defective regions. The density of pixels along the analyzed profile lines has yielded enhancement by a factor of approximately two for the reconstructed images as compared to the original images. We tested the SSC-GSM method on GD-Xray database with 68 radiographs of the weld. In total, the SSC-GSM technique can improve the contrast of radiography image by back ground removal method and show the defects better that exist in weld radiographs, compared to traditional method for the detection of weld defects.

Intention recognition-based human–machine interaction for mixed flow assembly

Mixed-flow assembly provides a highly adaptable solution for production processes, catering to the extensive customization requirements in product manufacturing. Human–machine interaction (HMI) can significantly enhance the efficiency, flexibility, and responsiveness of mixed-flow production lines by enabling operators to collaborate with machines. However, current HMI research primarily focuses on temporal or spatial interaction, where tasks are completed independently by the operator and machine in a predetermined sequence, with emphasis on collision avoidance in a shared workspace. Research on spatial–temporal HMI is currently lacking. This paper addresses this gap through three comprehensive steps. Firstly, we develop an intention recognition model based on Gaussian mixture distribution to effectively identify the user’s operational intention. Subsequently, we design a hybrid industrial communication architecture to facilitate intent sharing among various production elements. Finally, an empirical study is conducted to assess the impact of different forms of HMI on assembly efficiency and error rates. Our experimental results demonstrate that spatial–temporal HMI can enhance assembly efficiency by approximately 15% and reduce the defective rate. In future studies, the proposed spatial–temporal cooperation platform could integrate additional perception technologies to alleviate assembly fatigue and improve operators’ well-being.

Robust Frontal Vehicle Pose Estimation Based on Structural Parameter Optimization Using Reliable Edge Point Sequences

In order to enhance the stability of vehicle pose estimation within driving videos, a novel methodology for optimizing vehicle structural parameters is introduced. This approach hinges on evaluating the reliability of edge point sequences. Firstly, a multi−task and iterative convolutional neural network (MI−CNN) is constructed, enabling the simultaneous execution of four critical tasks: vehicle detection, yaw angle prediction, edge point location, and visibility assessment. Secondly, an imperative aspect of the methodology involves establishing a local tracking search area. This region is determined by modeling the limitations of vehicle displacement between successive frames. Vehicles are matched using a maximization approach that leverages point similarity. Finally, a reliable edge point sequence plays a pivotal role in resolving structural parameters robustly. The Gaussian mixture distribution of vehicle distance change ratios, derived from two measurement models, is employed to ascertain the reliability of the edge point sequence. The experimental results showed that the mean Average Precision (mAP) achieved by the MI−CNN network stands at 89.9%. A noteworthy observation is that the proportion of estimated parameters whose errors fall below the threshold of 0.8 m consistently surpasses the 85% mark. When the error threshold is set at less than 0.12 m, the proportion of estimated parameters meeting this criterion consistently exceeds 90%. Therefore, the proposed method has better application status and estimation precision.