Mixture Of Density Functions Research Articles

Fisher and Bayes-Fisher information measures for finite mixture distributions

. In this work, we consider Fisher information and Bayes-Fisher information measures for the mixing parameter vector of a finite mixture density function and develop some associated results for this model. We provide several interesting connections between these measures and some known informational measures, such as chi-square divergence, Shannon entropy, Kullback-Leibler, Jeffreys, and Jensen-Shannon divergences. Finally, to demonstrate the usefulness of the Bayes-Fisher information measure, we apply it to a real example in image processing and present some numerical results. Our findings in this regard show that this information measure is an effective criteria for quantifying the similarity between two images.

Fisher information and its extensions based on infinite mixture density functions

In this work, we consider the Fisher information and some of its well-known extended versions and then establish some results based on infinite mixture density functions for the proposed information measures. Specifically we introduce the Jensen-type of Fisher information (parametric-type and density-based) and generalized Fisher information measures based on infinite mixture density functions. We then show that the proposed Jensen–Fisher information measure have two representations in terms of Fisher information distance in the both parametric-type and density-based cases. We have further shown that the generalized Fisher information of an infinite mixture density can be stated based on Pearson–Vajda χk divergence. Finally, we examine the convexity property of q−Fisher information measure based on finite mixture density functions under a mild condition. Some examples related to scale mixture of skew-normal family of distributions, with emphasis on skew-normal density, are illustrated within the paper.

Endogenous Household Classification: Russian Regions

In order to study the structure of society, sociologists usually distinguish several homogeneous social groups, or classes. The most common division consists of three groups: upper, middle and lower classes. Such a partition is traditionally based on a subjective (exogenous) criteria adopted by a particular researcher. In this paper, the distribution of households in Russian federal districts is modeled as a mixture of three lognormal distributions. The mixing proportions (probabilities) of the mixture components and the corresponding distribution parameters are modeled as functions of the individual characteristics of households. The result is an endogenous decomposition of household sample into three clusters (lower, middle, upper). This classification allows analyzing the difference between regions and the patterns of intergroup dynamics in the period 2014—2018. The approach used in this work has demonstrated great flexibility in analyzing the distribution of income, the dynamics of this distribution over time, as well as a migration between relatively homogeneous clusters. The use of mixture density function with endogenously determined probabilities allows for precise detection of the effects of the income heterogeneity determinants within each cluster.

Bayesian inference from the mixture of half-normal distributions under censoring

This study considers the Bayesian inference for the mixture of two components of half-normal distribution using non-informative and informative prior. Several of its structural properties were derived, including explicit expression for mean, median, mode, reliability and hazard rate functions. Due to cost and time constraints, in most lifetime testing experiments censoring is an obligatory feature of lifetime datasets. We investigated Bayesian estimation of the parameters using various loss functions. The prior belief of the mixture model is represented by the uniform and square-root inverted gamma priors. Some properties of the model with graphs of the mixture density and hazard function are also discussed. The efficiencies of the proposed set of estimates of the mixture model parameters were studied through simulation and a real life dataset. Posterior risks of the Bayes estimators are evaluated and compared to explore the effect of prior belief and loss functions.

Diagnosis of sucker rod pumping based on dynamometer card decomposition and hidden Markov model

In oil field production, dynamometer card is the key source of information to analyze the down-hole operating conditions of sucker rod pumping. However, under different operating conditions, most of the existing diagnostic technologies are incapable to extract features from dynamometer cards automatically and comprehensively. Based on the mechanism analysis of dynamometer card, a useful diagnostic method with novel feature extraction method is proposed for diagnosing the operating condition of sucker rod pumping. A novel barycentric decomposition strategy is applied to divide the dynamometer cards, which can automatically adjust divided regions according to the shape change of dynamometer card. The curve moments are extracted from the parts of divided results to obtain the comprehensive features for the follow-up algorithm. Subsequently, the hidden Markov model with mixture density function is designed as a classifier to map the relationship between the operating condition and the features of dynamometer card. This technique is successfully carried out in a fault dynamometer card atlas that is collected from productive field. Finally, the experimental results confirm the validity of the proposed diagnosis approach.

Estimation of the Optimal HMM Parameters for Amazigh Speech Recognition System Using CMU-Sphinx

In this paper, we are looking for the optimal value of number of Hidden Markov Models (HMMs) states, and number of Gaussian mixture density functions for Amazigh automated speech recognition system. This system is based on the open source CMU Sphinx-4, from the Carnegie Mellon University. CMU Sphinx is a large-vocabulary; speaker-independent, continuous speech recognition system based on HMMs. the acoustic model is generally an HMMs, typically a three-state left-right HMM called Bakis It is perfectly adapted to the speech in its temporal progress since. the corpus of training consists of 11220 audio files. The test-data used for evaluating the system-performance consists of 1320 audio files. The performance of ASR is evaluate by the Word Error Rate WER, and results are compared to previous work.

Mathematical Modeling and Evaluation of Human Motions in Physical Therapy Using Mixture Density Neural Networks

The objective of the proposed research is to develop a methodology for modeling and evaluation of human motions, which will potentially benefit patients undertaking a physical rehabilitation therapy (e.g., following a stroke or due to other medical conditions). The ultimate aim is to allow patients to perform home-based rehabilitation exercises using a sensory system for capturing the motions, where an algorithm will retrieve the trajectories of a patient's exercises, will perform data analysis by comparing the performed motions to a reference model of prescribed motions, and will send the analysis results to the patient's physician with recommendations for improvement. The modeling approach employs an artificial neural network, consisting of layers of recurrent neuron units and layers of neuron units for estimating a mixture density function over the spatio-temporal dependencies within the human motion sequences. Input data are sequences of motions related to a prescribed exercise by a physiotherapist to a patient, and recorded with a motion capture system. An autoencoder subnet is employed for reducing the dimensionality of captured sequences of human motions, complemented with a mixture density subnet for probabilistic modeling of the motion data using a mixture of Gaussian distributions. The proposed neural network architecture produced a model for sets of human motions represented with a mixture of Gaussian density functions. The mean log-likelihood of observed sequences was employed as a performance metric in evaluating the consistency of a subject's performance relative to the reference dataset of motions. A publically available dataset of human motions captured with Microsoft Kinect was used for validation of the proposed method. The article presents a novel approach for modeling and evaluation of human motions with a potential application in home-based physical therapy and rehabilitation. The described approach employs the recent progress in the field of machine learning and neural networks in developing a parametric model of human motions, by exploiting the representational power of these algorithms to encode nonlinear input-output dependencies over long temporal horizons.

An Improved Gaussian Mixture CKF Algorithm under Non-Gaussian Observation Noise

In order to solve the problems that the weight of Gaussian components of Gaussian mixture filter remains constant during the time update stage, an improved Gaussian Mixture Cubature Kalman Filter (IGMCKF) algorithm is designed by combining a Gaussian mixture density model with a CKF for target tracking. The algorithm adopts Gaussian mixture density function to approximately estimate the observation noise. The observation models based on Mini RadaScan for target tracking on offing are introduced, and the observation noise is modelled as glint noise. The Gaussian components are predicted and updated using CKF. A cost function is designed by integral square difference to update the weight of Gaussian components on the time update stage. Based on comparison experiments of constant angular velocity model and maneuver model with different algorithms, the proposed algorithm has the advantages of fast tracking response and high estimation precision, and the computation time should satisfy real-time target tracking requirements.

Numerical Study of the Effect of Staged Gun and Quarl on the Performance of Low-NOx Burners

AbstractThree-dimensional numerical simulations were carried out to study fuel-staged low-NOx burners (LNB). The effect of the number of staged guns (four and six) and quarl style (Venturi and boss) on the performance of the LNBs was investigated. The flow field, flame temperature, OH radical field, and NO emission were analyzed. The turbulence, radiation, and chemical reactions were simulated with the standard k-e model, discrete ordinate (DO) model, and probability density function mixture fraction model, respectively, using a commercial computational fluid dynamics code. The numerical model was validated with experimental measurements at different excess air conditions. The agreement of the calculated and measured NO emission is remarkable; therefore, the present model is considered reliable. The results indicate that the number of staged guns has little effect on the NO emission; the boss quarl increases mean air velocity, changes staged gas flow direction, and reduces peak flame temperature and peak ...

Using mixture density functions for modelling of wage distributions

This article explores the possibility of modeling the wage distribution using a mixture of density functions. We deal with this issue for a long time and we build on our earlier work. Classical models use the probability distribution such as normal, lognormal, Pareto, etc., but the results are not very good in the last years. Changing the parameters of a probability density over time has led to a degradation of such models and it was necessary to choose a different probability distribution. We were using the idea of mixtures of distributions (instead of using one classical density) in previous articles. We tried using a mixture of probability distributions (normal, lognormal and a mixture of Johnson’s distribution densities) in our models. The achieved results were very good. We used data from Czech Statistical Office covering the wages of the last 18 years in Czech Republic.

Stability Analysis of Coupled Heat and Mass Transfer Boundary Layers During Steam–Solvent Oil Recovery Process

Convective mixing at the edge of the steam chamber enhances heat and mass transfer rates, which increases oil mobility and production rate. A linear stability analysis is performed under transient concentration and steady-state temperature boundary layers with temperature and concentration dependent fluid density and viscosity. It is found that the critical Rayleigh number depends on coefficients of the mixture viscosity and density function. Results show that the onset of instability is delayed as the concentration and temperature dependency of the solvent–oil mixture viscosity increases. Different potential solvents for heavy oil recovery are compared based on the critical time of instability. It is shown that intermediate molecular weight solvents lead to stronger convection, which is in agreement with experimental observations reported in the literature. These results are applicable for optimum design of laboratory experiments and selection of appropriate additives to steam for design of field- scale heavy oil recovery process.

The Statistical Properties of Filtered Signals

In this paper, the statistical properties of filtered or convolved signals are considered by deriving the resulting density functions as well as the exact mean and variance expressions given a prior knowledge about the statistics of the individual signals in the filtering or convolution process. It is shown that the density function after linear convolution is a mixture density, where the number of density components is equal to the number of observations of the shortest signal. For circular convolution, the observed samples are characterized by a single density function, which is a sum of products. Keywords—Circular Convolution, linear Convolution, mixture density function. NOTATION A signal is a group of observations, and these are represented in vector form. For example, xi(n) = [xi(1), xi(2), · · · , xi(Ki)] is a vector for the i signal, for i [1, N ], whose observations are xi(n), for n [1,Ki], where Ki is the length of the i signal. Given a vector xi(n), the variable Xi (capital letter with a corresponding subscript) is defined where its possible values are the vector elements or observations, and for Xi we define the density function p(xi) summarizing the statistical properties of its observations.

Selection of suitable prior for the Bayesian mixture of a class of lifetime distributions under type-I censored datasets

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration.

Blind source separation of ship-radiated noise based on generalized Gaussian model

When the distribution of the sources cannot be estimated accurately, the ICA algorithms failed to separate the mixtures blindly. The generalized Gaussian model (GGM) is presented in ICA algorithm since it can model non-Gaussian statistical structure of different source signals easily. By inferring only one parameter, a wide class of statistical distributions can be characterized. By using maximum likelihood (ML) approach and natural gradient descent, the learning rules of blind source separation (BSS) based on GGM are presented. The experiment of the ship-radiated noise demonstrates that the GGM can model the distributions of the ship-radiated noise and sea noise efficiently, and the learning rules based on GGM gives more successful separation results after comparing it with several conventional methods such as high order cumulants and Gaussian mixture density function.

Finite Mixture Dynamic Regression Modeling of Panel Data With Implications for Dynamic Response Analysis

This article considers the problem of estimating dynamic linear regression models when the data are generated from finite mixture probability density function where the mixture components are characterized by different dynamic regression model parameters. Specifically, conventional linear models assume that the data are generated by a single probability density function characterized by a single set of regression model parameters. However, when the true generating model is finite mixture density function, then estimation of conventional linear models under the assumption of a single density function may lead to erroneous conclusions. Instead, it may be desirable to estimate the regression model under the assumption that the data are derived from a finite mixture density function and to examine differences in the parameters of the model within each mixture component. Dynamic regression models and subsequent dynamic response analysis using dynamic multipliers are also likely to be affected by the existence of a finite mixture density because dynamic multipliers are functions of the regression model parameters. Utilizing finite mixture modeling applied to two real data examples, this article shows that dynamic responses to changes in exogenous variables can be quite different depending on the number and nature of underlying mixture components. Implications for substantive conclusions based on the use of dynamic multipliers is discussed.

The use of a mixture of probability distributions in temperature interlaboratory comparisons

Several studies highlight the need for appropriate statistical and probabilistic tools to analyse the data provided by the participants in an interlaboratory comparison. In some temperature comparisons, where the measurand is a physical state, independent realizations of the same physical state are acquired in each participating institute, which should be considered as belonging to a single super-population. This paper introduces the use of a probabilistic tool, a mixture of probability distributions, to represent the overall population in such a temperature comparison. This super-population is defined by combining the local populations in given proportions. The mixture density function identifies the total data variability, and the key comparison reference value has a natural definition as the expectation value of this probability density.

The algorithm of decomposing superimposed 2-D Poisson processes and its application to the extracting earthquake clustering pattern

Aiming at the complexity of seismic gestation mechanism and spatial distribution, we hypothesize that the seismic data are composed of background earthquakes and anomaly earthquakes in a certain temporal-spatial scope. Also the background earthquakes and anomaly earthquakes both satisfy the 2-D Poisson process of different parameters respectively. In the paper, the concept ofN-th order distance is introduced in order to transform 2-D superimposed Poisson process into 1-D mixture density function. On the basis of choosing the distance, mixture density function is decomposed to recognize the anomaly earthquakes through genetic algorithm. Combined with the temporal scanning ofC value, the algorithm is applied to the recognition on spatial pattern of foreshock anomalies by examples of Songpan and Longling sequences in the southwest of China.

Restructuring Gaussian mixture density functions in speaker-independent acoustic models

In continuous speech recognition featuring hidden Markov model (HMM), word N-gram, and time-synchronous beam search, a local modeling mismatch in the HMM will often cause the recognition performance to degrade. To cope with this problem, this paper proposes a method of restructuring Gaussian mixture output probability density functions (pdfs) in a pre-trained speaker-independent HMM set based on speech data. In this method, Gaussians are copied from other mixture pdfs, taking the distribution of local errors into account. This method leads to a restructuring of the mixture pdfs, where some Gaussians are shared by several states and the total number of Gaussians is not modified. Furthermore, the distribution of local errors is extracted by comparing the pre-trained HMM set and the speech data used in the pre-training, and thus new training data are not needed for this restructuring method. Experimental results prove that the proposed restructuring method can effectively restore local modeling mismatches and improve recognition performance.

Fast iterative segmentation of high resolution medical images

Various applications in positron emission tomography (PET), single photon emission computed tomography (SPECT) and magnetic resonance imaging (MRI) require segmentation of 20 to 60 high resolution images of size 256/spl times/256 pixels in 3-9 seconds per image. This places particular constraints on the design of image segmentation algorithms. This paper proposes a quantized data representation and a quantised EM algorithm for estimating the parameters of a finite mixture density function to be used in a Bayes classifier for image segmentation. Both a Monte Carlo evaluation and an application to MRI images showed that the quantized EM algorithm can dramatically reduce the required computation time with negligible difference in mean estimation error and mean classification error.

A Neural Network model in stereovision matching

The paper outlines a method for solving the stereovision matching problem through a Neural Network approach based on self-organizing technique. The goal is to classify pairs of features (edge segments) as true or false matches; giving rise to two classes. Thus, the corresponding parameter vector from two component density functions, representing both classes and drawn as Normal densities, are to be estimated by using an unsupervised learning method. A three layer neural network topology implements the mixture density function and Bayes's rule, all required computations are realized with the simple “sum of product” units commonly used in connectionist models. The unsupervised learning method leads to a learning rule, while all applicable constraints from stereovision field yield an activation rule. A training process receives the samples to learn, and a matching process classifies the pairs. The method is illustrated with two images from an indoor scene.