Distribution Of Compounds Research Articles

Robust Kalman Filters Based on Gaussian Scale Mixture Distributions With Application to Target Tracking

In this paper, a new robust Kalman filtering framework for a linear system with non-Gaussian heavy-tailed and/or skewed state and measurement noises is proposed through modeling one-step prediction and likelihood probability density functions as Gaussian scale mixture (GSM) distributions. The state vector, mixing parameters, scale matrices, and shape parameters are simultaneously inferred utilizing standard variational Bayesian approach. As the implementations of the proposed method, several solutions corresponding to some special GSM distributions are derived. The proposed robust Kalman filters are tested in a manoeuvring target tracking example. Simulation results show that the proposed robust Kalman filters have a better estimation accuracy and smaller biases compared to the existing state-of-the-art Kalman filters.

Nonlinear state-space system identification with robust laplace model

This paper investigates a robust identification solution for the nonlinear state-space model in which the outputs are polluted by unknown outliers. The problem of outliers is frequently encountered in practical industries that can greatly challenge the modelling of industrial processes. In order to overcome the obstacles brought by the outliers, the heavy-tailed Laplace distribution is applied to describe the output measurement process. Specifically, the Laplace distribution can be decomposed as a scale mixture of Gaussian distributions, which makes it robust for the outliers. The unknown model parameters are estimated with the expectation–maximisation algorithm while the particle smoother is used to solve the latent state estimation problem. The usefulness and robustness of the proposed algorithm are verified through the numerical examples including the model of a common chemical process.

An Entropy-Based Algorithm with Nonlocal Residual Learning for Image Compressive Sensing Recovery

Image recovery from compressive sensing (CS) measurement data, especially noisy data has always been challenging due to its implicit ill-posed nature, thus, to seek a domain where a signal can exhibit a high degree of sparsity and to design an effective algorithm have drawn increasingly more attention. Among various sparsity-based models, structured or group sparsity often leads to more powerful signal reconstruction techniques. In this paper, we propose a novel entropy-based algorithm for CS recovery to enhance image sparsity through learning the group sparsity of residual. To reduce the residual of similar packed patches, the group sparsity of residual is described by a Laplacian scale mixture (LSM) model, therefore, each singular value of the residual of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter, to exploit the benefits of high-order dependency among sparse coefficients. Due to the latent variables, the maximum a posteriori (MAP) estimation of the sparse coefficients cannot be obtained, thus, we design a loss function for expectation–maximization (EM) method based on relative entropy. In the frame of EM iteration, the sparse coefficients can be estimated with the denoising-based approximate message passing (D-AMP) algorithm. Experimental results have shown that the proposed algorithm can significantly outperform existing CS techniques for image recovery.

Bayesian modeling of the structural connectome for studying Alzheimer’s disease

We study possible relations between the structure of the connectome, white matter connecting different regions of brain, and Alzheimer disease. Regression models in covariates including age, gender and disease status for the extent of white matter connecting each pair of regions of brain are proposed. Subject We study possible relations between the Alzheimer's disease progression and the structure of the connectome, white matter connecting different regions of brain. Regression models in covariates including age, gender and disease status for the extent of white matter connecting each pair of regions of brain are proposed. Subject inhomogeneity is also incorporated in the model through random effects with an unknown distribution. As there are large number of pairs of regions, we also adopt a dimension reduction technique through graphon (Lovasz and Szegedy (2006)) functions, which reduces functions of pairs of regions to functions of regions. The connecting graphon functions are considered unknown but assumed smoothness allows putting priors of low complexity on them. We pursue a nonparametric Bayesian approach by assigning a Dirichlet process scale mixture of zero mean normal prior on the distributions of the random effects and finite random series of tensor products of B-splines priors on the underlying graphon functions. Markov chain Monte Carlo techniques, for drawing samples for the posterior distributions are developed. The proposed Bayesian method overwhelmingly outperforms similar ANCOVA models in the simulation setup. The proposed Bayesian approach is applied on a dataset of 100 subjects and 83 brain regions and key regions implicated in the changing connectome are identified.

On the Mayer Series of Two-Dimensional Yukawa Gas at Inverse Temperature in the Interval of Collapse

A Theorem on the minimal specific energy for a system with \pm 1 charged particles interacting through the Yukawa pair potential v is proved which may stated as follows. Let v be represented by scale mixtures of d-dimensional Euclid's hat (cutoff at short scale distances) with d\geq 2. For any even number of particles n, the interacting energy U_{n} divided by n, attains an n-independent minimum at a configuration with zero net charge and particle positions collapsed altogether to a point. For any odd number of particles n, the ratio U_{n}/(n-1) attains its minimum value, the same of the previous cases, at the configuration with \pm 1 net charge and particle positions collapsed to a point. This Theorem is then used to resolve an obstructive remark of an unpublished paper (Remark 7.5 of \cite{Guidi-Marchetti}) which, whether the standard decomposition of the Yukawa potential into scales were adopted, would impede a direct proof of the convergence of the Mayer series of the two-dimensional Yukawa gas for the inverse temperature in the whole interval [4\pi ,8\pi ) of collapse. In the present paper, it is proven convergence up to the second threshold 6\pi and its given explanations on the mechanism that allow it to be extend up to 8\pi . The paper distinguishes the matters concerning stability from those related to convergence of the Mayer series. In respect to the latter the paper dedicates to the Cauchy majorante method applied to the density function of Yukawa gas in the interval of collapses. It also dedicates to the proof of the main Theorem and estimates of the modified Bessel functions of second kind involved in both representations of two-dimensional Yukawa potential: standard and scale mixture of the Euclid's hat function.

Multivariate tail conditional expectation for scale mixtures of skew-normal distribution

ABSTRACTIn practice, a financial or actuarial data set may be a skewed or heavy-tailed and this motivates us to study a class of distribution functions in risk management theory that provide more information about these characteristics resulting in a more accurate risk analysis. In this paper, we consider a multivariate tail conditional expectation (MTCE) for multivariate scale mixtures of skew-normal (SMSN) distributions. This class of distributions contains skewed distributions and some members of this class can be used to analyse heavy-tailed data sets. We also provide a closed form for TCE in a univariate skew-normal distribution framework. Numerical examples are also provided for illustration.

Quantile forecasting based on a bivariate hysteretic autoregressive model with GARCH errors and time ‐varying correlations

AbstractTo understand and predict chronological dependence in the second‐order moments of asset returns, this paper considers a multivariate hysteretic autoregressive (HAR) model with generalized autoregressive conditional heteroskedasticity (GARCH) specification and time‐varying correlations, by providing a new method to describe a nonlinear dynamic structure of the target time series. The hysteresis variable governs the nonlinear dynamics of the proposed model in which the regime switch can be delayed if the hysteresis variable lies in a hysteresis zone. The proposed setup combines three useful model components for modeling economic and financial data: (1) the multivariate HAR model, (2) the multivariate hysteretic volatility models, and (3) a dynamic conditional correlation structure. This research further incorporates an adapted multivariate Student t innovation based on a scale mixture normal presentation in the HAR model to tolerate for dependence and different shaped innovation components. This study carries out bivariate volatilities, Value at Risk, and marginal expected shortfall based on a Bayesian sampling scheme through adaptive Markov chain Monte Carlo (MCMC) methods, thus allowing to statistically estimate all unknown model parameters and forecasts simultaneously. Lastly, the proposed methods herein employ both simulated and real examples that help to jointly measure for industry downside tail risk.

EM-test for homogeneity in a two-sample problem with a mixture structure

ABSTRACTIn many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials, a two-sample problem with one of the samples having a mixture structure often arises. Due to the importance and wide applications of scale mixtures and location mixtures, we consider in this paper the case that the component densities differ only in scale parameters and the case that the component densities differ only in location parameters, and further construct an EM-test for the two-sample problem under each case. We show that both the EM-tests possess a chi-squared null limiting distribution. The local power analysis and sample size calculations are also investigated. Finally, the simulation studies and real data analysis demonstrate that the proposed EM-tests have better performance than the existing methods.

Analysis of the Causes of Tube and Pipeline Blocking in Sulige Gas Field

A large number of blockage appeared in gas wells and pipeline appeared, which causedplugging, corrosion and the increasing of wellbore pressure difference, and seriously affect thenormal production of gas well of problems. In this paper, the water quality of produced water fromthe severe cases of single wells or pipeline water were analyzed, also include the composition ofblockage and core with the chemical volumetric method (CVM) , X-Ray Diffraction (XRD) and x-rayfluorescence (XFS) method. Meanwhile, the core powder was leached in simulated acid worksolution, and then the leaching solution was analyzed with CVM. The experimental results show thatThe produced water has high salinity, high contents of Ca2+, Ba2+ and Sr2+, low pH value, which leadto corrosion and scaling. The main components of the blockage are acid insoluble strontium sulfate(barium) scale or corrosion product or mixture of corrosion and CaCO3 scaling product. Ca2+, Ba2+and Sr2+ were easy to scale in wellbore or pipeline when they encountered other produced water fromdifferent formation. The Ca2+, Mg2+, Ba2+, Sr2+ and Fe 2+/3+ mainly derived from the dissolution offormation debris in formation water and working fluid (especially acidic working fluid) to reservoirrock, so the salinity of the produced water increased, and the trend of scaling and corrosion alsoincreased with the gas field development.

Gaussian Mixture Representation of the Laplace Distribution Revisited: Bibliographical Connections and Extensions

We provide bibliographical connections and extensions of several representations of the classical Laplace distribution, discussed recently in the study of Ding and Blitzstein. Beyond presenting relation to some previous results, we also include their skew as well as multivariate versions. In particular, the distribution of det Z, where Z is an n × n matrix of iid standard normal components, is obtained for an arbitrary integer n. While the latter is a scale mixture of Gaussian distributions, the Laplace distribution is obtained only in the case n = 2. Supplementary materials for this article are available online.

Orthogonality-Promoting Dictionary Learning via Bayesian Inference

Dictionary Learning (DL) plays a crucial role in numerous machine learning tasks. It targets at finding the dictionary over which the training set admits a maximally sparse representation. Most existing DL algorithms are based on solving an optimization problem, where the noise variance and sparsity level should be known as the prior knowledge. However, in practice applications, it is difficult to obtain these knowledge. Thus, non-parametric Bayesian DL has recently received much attention of researchers due to its adaptability and effectiveness. Although many hierarchical priors have been used to promote the sparsity of the representation in non-parametric Bayesian DL, the problem of redundancy for the dictionary is still overlooked, which greatly decreases the performance of sparse coding. To address this problem, this paper presents a novel robust dictionary learning framework via Bayesian inference. In particular, we employ the orthogonality-promoting regularization to mitigate correlations among dictionary atoms. Such a regularization, encouraging the dictionary atoms to be close to being orthogonal, can alleviate overfitting to training data and improve the discrimination of the model. Moreover, we impose Scale mixture of the Vector variate Gaussian (SMVG) distribution on the noise to capture its structure. A Regularized Expectation Maximization Algorithm is developed to estimate the posterior distribution of the representation and dictionary with orthogonality-promoting regularization. Numerical results show that our method can learn the dictionary with an accuracy better than existing methods, especially when the number of training signals is limited.

Bayesian variable selection using partially observed categorical prior information in fine-mapping association studies.

Several methods have been proposed to allow functional genomic information to inform prior distributions in Bayesian fine-mapping case-control association studies. None of these methods allow the inclusion of partially observed functional genomic information. We use functional significance (FS) scores that combine information across multiple bioinformatics sources to inform our effect size prior distributions. These scores are not available for all single-nucleotide polymorphisms (SNPs) but by partitioning SNPs into naturally occurring FS score groups, we show how missing FS scores can easily be accommodated via finite mixtures of elicited priors. Most current approaches adopt a formal Bayesian variable selection approach and either limit the number of causal SNPs allowed or use approximations to avoid the need to explore the vast parameter space. We focus instead on achieving differential shrinkage of the effect sizes through prior scale mixtures of normals and use marginal posterior probability intervals to select candidate causal SNPs. We show via a simulation study how this approach can improve localisation of the causal SNPs compared to existing mutli-SNP fine-mapping methods. We also apply our approach to fine-mapping a region around the CASP8 gene using the iCOGS consortium breast cancer SNP data.

A robust class of homoscedastic nonlinear regression models

ABSTRACTIn this paper, we examine a nonlinear regression (NLR) model with homoscedastic errors which follows a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The objective of using this family is to develop a robust NLR model. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and lightly/heavy-tailed distributions and is an alternative family to the well-known scale mixtures of skew-normal (SMSN) family studied by Branco and Dey [35]. A key feature of this study is using a new suitable hierarchical representation of the family to obtain maximum-likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and some natural real datasets and also compared to other well-known NLR models.

Generalized negative binomial distributions as mixed geometric laws and related limit theorems*

In this paper, we study a wide and flexible family of discrete distributions, the so-called generalized negative binomial (GNB) distributions, which are mixed Poisson distributions with the mixing laws belonging to the class of generalized gamma (GG) distributions. This family was introduced by E.W. Stacy as a particular family of lifetime distributions containing gamma, exponential power, and Weibull distributions. These distributions seem to be very promising in the statistical description of many real phenomena and very convenient and almost universal models for the description of statistical regularities in discrete data. We study analytic properties of GNB distributions. We prove that a GG distribution is a mixed exponential distribution if and only if the shape and exponent power parameters are no greater than one. We write the mixing distribution explicitly as a scale mixture of strictly stable laws concentrated on the nonnegative half-line. As a corollary, we obtain a representation for the GNB distribution as a mixed geometric distribution. We consider the corresponding scheme of Bernoulli trials with random probability of success. Within this scheme, we prove a random analog of the Poisson theorem establishing the convergence of mixed binomial distributions to mixed Poisson laws. We prove limit theorems for random sums of independent random variables in which the number of summands has the GNB distribution and the summands have both light- and heavy-tailed distributions. We obtain that the class of limit laws is wide enough and includes the so-called generalized variance gamma distributions. We obtain various representations for the limit laws in terms of mixtures of Mittag-Leffler, Linnik, or Laplace distributions. We prove limit theorems establishing the convergence of the distributions of statistics constructed from samples with random sizes obeying the GNB distribution to generalized variance gamma distributions. We also discuss some applications of GNB distributions in meteorology.

Synthesis of calcium hydroxide for heritage conservation

This research aims to employ nanotechnology and spectroscopy in the field of heritage conservation. In this research nanomaterial (calcium hydroxide) used in conservation of manuscripts, paintings and relics because of their impact on reducing the pH of paper which is the basic reason for cellulosic fiber break. The study done in stages, where calcium hydroxide had prepared by chemical method and analysis it by using atomic force microscopes (AFM),scanning electron microscope (SEM), x-ray diffraction (XRD), infrared spectroscopy (FTIR) as a first stage. In the second phase, initialize and the preparation of samples and study the properties of synthetic and hardness and microscopic study of the state of fiber cellulosic. Third phase includes spraying the mixture of nanoparticles with the solvent (ethanol or brobanol) and then left to dry and studying their properties again, where the study proved the effectiveness of nano scale mixture to reduce the pH to a long-term period. This new style in dealing with manuscripts is clean and inexpensive.

Joint Sparse Aperture ISAR Autofocusing and Scaling via Modified Newton Method-Based Variational Bayesian Inference

For sparse aperture (SA) radar echoes, the coherence between the undersampled pulses is destroyed, which challenges the effectiveness of the traditional autofocusing and scaling in inverse synthetic aperture radar (ISAR) imaging. A novel Bayesian ISAR autofocusing and scaling algorithm for sparse aperture is proposed, which utilizes Laplacian scale mixture, as the sparse prior of ISAR image, and variational Bayesian inference based on the Laplacian approximation to derive its posterior. In addition, it learns the phase error, rotational velocity, and center of target from radar echo automatically during the reconstruction of ISAR image, so as to achieve ISAR autofocusing and scaling for SA. Because the parameters learning is not easy to converge with the undersampled data, a modified Newton method based on joint constraint of entropy and sparsity is proposed to guarantee fast convergence in a right direction. Experimental results based on both simulated and measured data validate the robustness of the proposed ISAR imaging algorithm against SA and noise.

Bayesian Zero-Inflated Negative Binomial Regression Based on Pólya-Gamma Mixtures.

Motivated by a study examining spatiotemporal patterns in inpatient hospitalizations, we propose an efficient Bayesian approach for fitting zero-inflated negative binomial models. To facilitate posterior sampling, we introduce a set of latent variables that are represented as scale mixtures of normals, where the precision terms follow independent Pólya-Gamma distributions. Conditional on the latent variables, inference proceeds via straightforward Gibbs sampling. For fixed-effects models, our approach is comparable to existing methods. However, our model can accommodate more complex data structures, including multivariate and spatiotemporal data, settings in which current approaches often fail due to computational challenges. Using simulation studies, we highlight key features of the method and compare its performance to other estimation procedures. We apply the approach to a spatiotemporal analysis examining the number of annual inpatient admissions among United States veterans with type 2 diabetes.

Dynamic Shrinkage Processes

SummaryWe propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute-by-minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods.

Negative CO2 emissions - An analysis of the retention times required with respect to possible carbon leakage

With present emissions the global CO2 budget associated with a maximum temperature increase of about 1.5–2 °C will likely be spent within a few decades, Thus, it will be very difficult or perhaps even impossible to meet the climate targets agreed upon in Paris only by decreasing emissions of greenhouse gases. Scenarios presented in the IPCC reports accommodate for this by introducing so-called negative CO2 emissions. The idea is that the cumulative CO2 emission budget will be exceeded, but that massive negative emissions, especially during the latter part of the century, will remove the surplus of CO2 in the atmosphere.A number of different Negative Emissions Technologies (NETs) have been proposed, including Biomass Energy with Carbon Capture and Storage (BECCS), afforestation/reforestation, altered agricultural practices, biochar production, enhanced weathering and direct air captured. However, many of the options proposed could be associated with carbon leakage which could compromise the purpose of negative emissions, e.g. storage in of carbon in growing/dead biomass that leaks to the atmosphere. Furthermore, it may be difficult to safely assess the long-term leakage rates. To reach the large negative emissions needed it is expected to require a mix of approaches having different expected retention times, and different safety in terms of leakage rates.Could the risk of leakage mean that we are just delaying the problem and transferring the problem to coming generations? The short answer to this is that it all depends on the leakage rates. Different leakage rates and mixes of leakage rates are investigated in the paper. For the case of a mixture of leakage time scales of 300, 1000 and 10,000 years and assuming that 80% or more was permanently stored, the contribution to the atmospheric stock was small, peaking at about 3 ppm CO2. It was concluded that leakage would not significantly compromise the benefits of negative emissions unless leakage is substantial and rapid. To quantify what could be meant by substantial and rapid, an example would be if 100% of the CO2 stored would leak out at a rate of the order of 1%/year.

Bayesian variable selection for mixed effects model with shrinkage prior

Recently, many shrinkage priors have been proposed and studied in linear models to address massive regression problems. However, shrinkage priors are rarely used in mixed effects models. In this article, we address the problem of joint selection of both fixed effects and random effects with the use of several shrinkage priors in linear mixed models. The idea is to shrink small coefficients to zero while minimally shrink large coefficients due to the heavy tails. The shrinkage priors can be obtained via a scale mixture of normal distributions to facilitate computation. We use a stochastic search Gibbs sampler to implement a fully Bayesian approach for variable selection. The approach is illustrated using simulated data and a real example.