Mixture Distribution Model Research Articles

New generalized poisson mixture model for bimodal count data with drug effect: An application to rodent brief-access taste aversion experiments.

Pharmacodynamic (PD) count data can exhibit bimodality and nonequidispersion complicating the inclusion of drug effect. The purpose of this study was to explore four different mixture distribution models for bimodal count data by including both drug effect and distribution truncation. An example dataset, which exhibited bimodal pattern, was from rodent brief‐access taste aversion (BATA) experiments to assess the bitterness of ascending concentrations of an aversive tasting drug. The two generalized Poisson mixture models performed the best and was flexible to explain both under and overdispersion. A sigmoid maximum effect (Emax) model with logistic transformation was introduced to link the drug effect to the data partition within each distribution. Predicted density‐histogram plot is suggested as a model evaluation tool due to its capability to directly compare the model predicted density with the histogram from raw data. The modeling approach presented here could form a useful strategy for modeling similar count data types.

Interval timing under a behavioral microscope: Dissociating motivational and timing processes in fixed-interval performance.

The distribution of latencies and interresponse times (IRTs) of rats was compared between two fixed-interval (FI) schedules of food reinforcement (FI 30s and FI 90s), and between two levels of food deprivation. Computational modeling revealed that latencies and IRTs were well described by mixture probability distributions embodying two-state Markov chains. Analysis of these models revealed that only a subset of latencies is sensitive to the periodicity of reinforcement, and prefeeding only reduces the size of this subset. The distribution of IRTs suggests that behavior in FI schedules is organized in bouts that lengthen and ramp up in frequency with proximity to reinforcement. Prefeeding slowed down the lengthening of bouts and increased the time between bouts. When concatenated, latency and IRT models adequately reproduced sigmoidal FI response functions. These findings suggest that behavior in FI schedules fluctuates in and out of schedule control; an account of such fluctuation suggests that timing and motivation are dissociable components of FI performance. These mixture-distribution models also provide novel insights on the motivational, associative, and timing processes expressed in FI performance. These processes may be obscured, however, when performance in timing tasks is analyzed in terms of mean response rates.

Modeling loss data using mixtures of distributions

In this paper, we propose an alternative approach for flexible modeling of heavy tailed, skewed insurance loss data exhibiting multimodality, such as the well-known data set on Danish Fire losses. Our approach is based on finite mixture models of univariate distributions where all K components of the mixture are assumed to be from the same parametric family. Six models are developed with components from parametric, non-Gaussian families of distributions previously used in actuarial modeling: Burr, Gamma, Inverse Burr, Inverse Gaussian, Log-normal, and Weibull. Some of these component distributions are already alone suitable to model data with heavy tails, but do not cover the case of multimodality. Estimation of the models with a fixed number of components K is proposed based on the EM algorithm using three different initialization strategies: distance-based, k-means, and random initialization. Model selection is possible using information criteria, and the fitted models can be used to estimate risk measures for the data, such as VaR and TVaR. The results of the mixture models are compared to the composite Weibull models considered in recent literature as the best models for modeling Danish Fire insurance losses. The results of this paper provide new valuable tools in the area of insurance loss modeling and risk evaluation.

Automatic time-domain velocity estimation based on an accelerated clustering method

Time-domain velocity and moveout parameters can be directly obtained from local event slopes, which are estimated on the prestack seismic gathers. In practice, there are always some errors in the estimated local slopes, especially in low signal-to-noise ratio (S/N) situations. Thus, subsurface velocity information may be hidden in the image domain spanned by velocity and other moveout parameters. We have developed an accelerated clustering algorithm to find cluster centers without prior information about the number of clusters. First, plane-wave destruction is implemented to estimate the local event slopes. For every sample in the seismic gathers, we obtain the estimations of velocity and its location in the image domain, according to the local event slopes. These mapped data points in the new domain exhibit the structure of groups. We represent these points by a mixture distribution model. Then, the cluster centers of the mixture distribution model are located, which correspond to maximum likelihood velocities of the main subsurface structures. Approximate velocity uncertainties bounds are used to select centers corresponding to reflections. Finally, interpolation is performed on the clustered unevenly sampled knot velocities to build the effective velocity model on regular grids. With synthetic and field data examples, we have determined that the proposed automatic velocity estimation method can give a stacking velocity model and a time migration velocity model with relatively high accuracy.

Non-stationary rainfall and natural flows modeling at the watershed scale

Summary In areas in which natural water resources are variable over time, tools that determine the probability distribution of hydrological variables are required to evaluate various management alternatives. In this article, a stochastic simulation framework of hydrological variables through atmospheric pressure modeling is proposed. This methodology employs the mean value of the atmospheric pressure in the winter to differentiate the wet, medium and dry years in terms of rainfall and flow at different temporal scales. Monthly mean and daily maximum rainfall and flow data series are stochastically replicated. To achieve this replication, a non-stationary parametric mixture distribution model that combines a Weibull and a Normal distribution is fitted to the univariate distribution of the atmospheric pressure. This model includes interannual variability through two covariables: extraterrestrial solar radiation and the NAO index. This model is applied to the Guadalete River Basin in southern Spain, in which the river flow regime is influenced by the highly seasonal precipitation regime typically found in the Mediterranean area. The non-stationary parametric mixture distribution model with the two covariables showed a good fit to the observed sea level pressure, displaying an important reduction on the BIC. A good correlation was obtained between the average sea level pressure in winter and the accumulated precipitation and flow ( r = −0.8 for monthly values and −0.6 for maximum daily values). The statistical similarity indicated that the synthetic series of precipitation and flow preserved the distribution trends in the observed data. The identical methodology can be applied in other watersheds once the direct relationship between the mean atmospheric pressure and the hydrology of the area is known.

Psychometric Evaluation and Discussions of English Language Learners’ Listening Comprehension

The importance of listening in the context of English language acquisition is gaining acceptance, but its unique attributes in language performance, while substantively and qualitatively justifiable, are generally not psychometrically defined. This article psychometrically supports listening as a distinct domain among the three other domains of language learning—reading, writing, and speaking—through the analysis of listening data from a large-scale K-12 English language proficiency assessment. Student responses in this study were compared on the basis of cognitive, metacognitive, and other learning strategies between high achieving and low achieving listening groups that were formed using a latent mixture distribution model. Latent mixture distribution and differential items functioning analyses together with classical item analysis were used to substantiate or draw attention to literature findings. The article also highlights the importance of social-interactive items that are inadvertently embedded in an assessment that is primarily created to measure academic language.

Testing Students with Special Educational Needs in Large-Scale Assessments - Psychometric Properties of Test Scores and Associations with Test Taking Behavior.

Assessing competencies of students with special educational needs in learning (SEN-L) poses a challenge for large-scale assessments (LSAs). For students with SEN-L, the available competence tests may fail to yield test scores of high psychometric quality, which are—at the same time—measurement invariant to test scores of general education students. We investigated whether we can identify a subgroup of students with SEN-L, for which measurement invariant competence measures of adequate psychometric quality may be obtained with tests available in LSAs. We furthermore investigated whether differences in test-taking behavior may explain dissatisfying psychometric properties and measurement non-invariance of test scores within LSAs. We relied on person fit indices and mixture distribution models to identify students with SEN-L for whom test scores with satisfactory psychometric properties and measurement invariance may be obtained. We also captured differences in test-taking behavior related to guessing and missing responses. As a result we identified a subgroup of students with SEN-L for whom competence scores of adequate psychometric quality that are measurement invariant to those of general education students were obtained. Concerning test taking behavior, there was a small number of students who unsystematically picked response options. Removing these students from the sample slightly improved item fit. Furthermore, two different patterns of missing responses were identified that explain to some extent problems in the assessments of students with SEN-L.

Robust unit commitment with $$n-1$$ n - 1 security criteria

The short-term unit commitment and reserve scheduling decisions are made in the face of increasing supply-side uncertainty in power systems. This has mainly been caused by a higher penetration of renewable energy generation that is encouraged and enforced by the market and policy makers. In this paper, we propose a two-stage stochastic and distributionally robust modeling framework for the unit commitment problem with supply uncertainty. Based on the availability of the information on the distribution of the random supply, we consider two specific models: (a) a moment model where the mean values of the random supply variables are known, and (b) a mixture distribution model where the true probability distribution lies within the convex hull of a finite set of known distributions. In each case, we reformulate these models through Lagrange dualization as a semi-infinite program in the former case and a one-stage stochastic program in the latter case. We solve the reformulated models using sampling method and sample average approximation, respectively. We also establish exponential rate of convergence of the optimal value when the randomization scheme is applied to discretize the semi-infinite constraints. The proposed robust unit commitment models are applied to an illustrative case study, and numerical test results are reported in comparison with the two-stage non-robust stochastic programming model.

Stochastic EM algorithm of a finite mixture model from hurdle Poisson distribution with missing responses

ABSTRACTIn this article, a finite mixture model of hurdle Poisson distribution with missing outcomes is proposed, and a stochastic EM algorithm is developed for obtaining the maximum likelihood estimates of model parameters and mixing proportions. Specifically, missing data is assumed to be missing not at random (MNAR)/non ignorable missing (NINR) and the corresponding missingness mechanism is modeled through probit regression. To improve the algorithm efficiency, a stochastic step is incorporated into the E-step based on data augmentation, whereas the M-step is solved by the method of conditional maximization. A variation on Bayesian information criterion (BIC) is also proposed to compare models with different number of components with missing values. The considered model is a general model framework and it captures the important characteristics of count data analysis such as zero inflation/deflation, heterogeneity as well as missingness, providing us with more insight into the data feature and allowing for dispersion to be investigated more fully and correctly. Since the stochastic step only involves simulating samples from some standard distributions, the computational burden is alleviated. Once missing responses and latent variables are imputed to replace the conditional expectation, our approach works as part of a multiple imputation procedure. A simulation study and a real example illustrate the usefulness and effectiveness of our methodology.

Bayesian semiparametric modeling of realized covariance matrices

This paper introduces several new Bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance (RCOV) matrices. Existing dynamic Wishart models are extended to countably infinite mixture models of Wishart and inverse-Wishart distributions. In addition to mixture models with constant weights we propose models with time-varying weights to capture time dependence in the unknown distribution. Each of our models can be combined with returns to provide a coherent joint model of returns and RCOV. The extensive forecast results show the new models provide very significant improvements in density forecasts for RCOV and returns and competitive point forecasts of RCOV.

A mixture model of size-biased distributions

In reliability and survival analysis, to model lifetime data, size-biased distributions are useful. In this paper, a mixture model of size-biased distributions is introduced and studied. Several reliability properties of this model are investigated. In addition, some implications of well-known stochastic orders and aging classes concerning the model are established. To underline the usefulness of the model, some examples of interest in reliability and statistics are given.

Mixture Distribution Fitting and Modeling for Regional Frequency Analysis of Maximum Wind Speed Over South Korea

본 연구에서는, L-moments와 Harmony Search 파라미터 추정법을 사용하여 지역빈도해석을 통한 한국 68개소의 설계풍속을 도출하는 연구를 실시하였다. 기존에 일반적으로 풍속 산정에 적용된 Generalized Logistic (GLOG), General Extreme Value (GEV), Generalized Pareto (GPAR), Weibull의 분포형에 적용하여 설계 풍속값을 산정하였을 뿐만 아니라 Gamma와 Gumbel의 분포를 조합시킨 혼합분포형을 이용하여서도 설계값을 산정하였다. 산정결과, 한국에서는 Weibull분포가 가장 적절한 분포모형임을 알 수 있었다. 기존에 적용되지 않았던 새로운 혼합형 분포형도 특정지역에서 충분히 사용가능한 분포형이 될 수 있음을 알 수 있었다. In this study, we tried to determine and investigate meteorologically homogeneous regions and to derive regional wind frequency estimates for 68 gauged sites in South Korea using an index wind method with L-moments and harmony search parameter estimation. Comparative regional wind frequency estimates were made for the tested region using various distributions, namely the Generalized Logistic (GLOG), General Extreme Value (GEV), Generalized Pareto (GPAR), Weibull. Furthermore, we applied three types of two-component mixture distributions, built by combination of Gumbel and Gamma distributions with five-parameters such as Gumbel-Gumbel (GumGum), Gamma-Gamma (GamGam), and Gamma-Gumbel (GamGum) distribution models. Their parameters are estimated by harmony search method (HS). The results of the current study showed that the Weibull distribution is identified as the bestfit distribution in Korea. In other words, Weibull as a suitable distribution with three parameters for other Korean stations.

Assessing consistency of fish survey data: uncertainties in the estimation of mackerel icefish (Champsocephalus gunnari) abundance at South Georgia

Mackerel icefish (Champsocephalus gunnari) is a semi-pelagic finfish species inhabiting shelf areas in the Southern Ocean. The population at South Georgia is currently exploited by pelagic trawlers fishing close to the seabed. Annual catches peaked at 150,000 t in 1983 and have declined since the mid-to-late 1980s. Bottom-trawl surveys have been conducted since 1987, providing a time series of abundance and size distribution for use in assessing the status of the stock and setting quotas. Food web models suggest that estimates of the biomass from survey data are substantially lower than the amount of icefish required by the local ecosystem. The aim of this study was to assess the uncertainty around current estimates of density and variance, using alternative nonparametric stratified bootstrapping methods. The stratified rescaling bootstrap estimator was identified as the most appropriate method of those tested: in comparison with the existing method, confidence intervals and the inter-annual variability of the estimates were reduced. Numbers-at-age were estimated from mixture distribution models fitted to length-disaggregated density data in order to determine whether individual cohorts were consistently detected by the surveys. Estimates of numbers-at-age could not consistently delineate cohorts in successive years indicating that survey-based estimates of density were biased. These biases may have arisen because the trawl gear did not select individuals of all sizes equally, or because sampling was restricted to the demersal component of the stock. Estimates of abundance of the pelagic component of the stock should be derived from acoustic data to improve the assessment.

Complex Non-rigid 3D Shape Recovery Using a Procrustean Normal Distribution Mixture Model

Recovering the 3D shape of a non-rigid object is a challenging problem. Existing methods make the low-rank assumption and do not scale well with the increased degree of freedom found in complex non-rigid deformations or shape variations. Moreover, in general, the degree of freedom of deformation is assumed to be known in advance, which limits the applicability of non-rigid structure from motion algorithms in a practical situation. In this paper, we propose a method for handling complex shape variations based on the assumption that complex shape variations can be represented probabilistically by a mixture of primitive shape variations. The proposed model is a generative probabilistic model, called a Procrustean normal distribution mixture model, which can model complex shape variations without rank constraints. Experimental results show that the proposed method significantly outperforms existing methods.

A finite mixture model of geometric distributions for lossless image compression

In this paper, we proposed a new geometric finite mixture model-based adaptive arithmetic coding (AAC) for lossless image compression. Applying AAC for image compression, large compression gains can be achieved only through the use of sophisticated models that provide more accurate probabilistic descriptions of the image. In this work, we proposed to divide the residual image into non-overlapping blocks, and then we model the statistics of each block by a mixture of geometric distributions of parameters estimated through the maximum likelihood estimation using the expectation–maximization algorithm. Moreover, a histogram tail truncation method within each predicted error block is used in order to reduce the number of symbols in the arithmetic coding and therefore to reduce the effect of the zero-occurrence symbols. Experimentally, we showed that using convenient block size and number of mixture components in conjunction with the prediction technique median edge detector, the proposed method outperforms the well known lossless image compressors.

Clustering of multivariate binary data with dimension reduction via L1-regularized likelihood maximization

Clustering methods with dimension reduction have been receiving considerable wide interest in statistics lately and a lot of methods to simultaneously perform clustering and dimension reduction have been proposed. This work presents a novel procedure for simultaneously determining the optimal cluster structure for multivariate binary data and the subspace to represent that cluster structure. The method is based on a finite mixture model of multivariate Bernoulli distributions, and each component is assumed to have a low-dimensional representation of the cluster structure. This method can be considered as an extension of the traditional latent class analysis. Sparsity is introduced to the loading values, which produces the low-dimensional subspace, for enhanced interpretability and more stable extraction of the subspace. An EM-based algorithm is developed to efficiently solve the proposed optimization problem. We demonstrate the effectiveness of the proposed method by applying it to a simulation study and real datasets.

A mixture model of global internet capacity distributions

This article develops a preferential attachment‐based mixture model of global Internet bandwidth and investigates it in the context of observed bandwidth distributions between 2002 and 2011. Our longitudinal analysis shows, among other things, that the bandwidth share distributions—and thus bandwidth differences—exhibit considerable path dependence where country proportions of international bandwidth in 2011 can be substantially accounted for by a preferential attachment‐based mixture of micro‐level processes. Our preferential attachment model, consistent with empirical data, does not predict increasing concentration of bandwidth within top‐ranked countries. We argue that recognizing the strong, but nuanced, historical inertia of bandwidth distributions is helpful in better discriminating among competing theoretical perspectives on the global digital divide as well as in clarifying policy discussions related to gaps between bandwidth‐rich and bandwidth‐poor countries.

Standard error estimation for mixed flood distributions with historic maxima

Flood frequency data from multiple sources can be modeled using finite mixture models of stationary distributions. Historic flood data can be incorporated into this framework using censored data methods. Most estimation methods treat historical flood records as typical realizations from the underlying distribution, although they can actually represent extrema. A review of these methods in a finite mixture framework and introduction of an approach that treats historical maxima as order statistics are presented as adaptations of an expectation conditional maximization algorithm to derive estimates for the finite mixture model. When information matrices are difficult to computse, Meilijson's (1989) score‐based approximation is used instead. The total derivative method is used to compute standard errors for low‐frequency quantiles for both traditional censored data methods and the new approach. The method is demonstrated on annual peak flow data using mixtures of lognormal and Gumbel distributions. Copyright © 2015 John Wiley & Sons, Ltd.

Bayesian Stable Mixture Model of State Densities of Generalized Chua's Circuit

In this paper, the probability density functions (PDFs) of the states of Generalized Chua's Circuit (GCC) have been modeled by Finite Mixture α-Stable (FMαS) distributions which is a Bayesian mixture model of α-stable distributions and it provides semiparametric characterization for the distributions of multiscroll chaotic attractors. Fully Bayesian approach has been applied to estimate the mixture parameters of multimodal distributions corresponding to the multiscroll chaotic attractors.

A new extended mixture model of residual lifetime distributions

In this paper, we first propose a new extended mixture model of residual lifetime distributions. We show that this model is suitable in modeling residual lifetime in some practical situations. Several closure properties of some well-known dependence concepts, stochastic orders and aging notions under the formation of this model, are obtained. Finally, preservation properties of some stochastic orders under the formation of the model are discussed and some examples of interest are presented.