Mixture Distribution Analysis Research Articles

Poisson mixture distribution analysis for North Carolina SIDS counts using information criteria


 
 
 Mixture distribution analysis provides us with a tool for identifying unlabeled clusters that naturally arise in a data set. In this paper, we demonstrate how to use the information criteria AIC and BIC to choose the optimal number of clusters for a given set of univariate Poisson data. We give an empirical comparison between minimum Hellinger distance (MHD) estimation and EM estimation for finding parameters in a mixture of Poisson distributions with artificial data. In addition, we discuss Bayes error in the context of classification problems with mixture of 2, 3, 4, and 5 Poisson models. Finally, we provide an example with real data, taken from a study that looked at sudden infant death syndrome (SIDS) count data from 100 North Carolina counties (Symons et al., 1983). This gives us an opportunity to demonstrate the advantages of the proposed model framework in comparison with the original analysis.
 

Nanoparticle tracking analysis and statistical mixture distribution analysis to quantify nanoparticle–vesicle binding

Nanoparticle tracking analysis (NTA) is a single particle tracking technique that in principle provides a more direct measure of particle size distribution compared to dynamic light scattering (DLS). Here, we demonstrate how statistical mixture distribution analysis can be used in combination with NTA to quantitatively characterize the amount and extent of particle binding in a mixture of nanomaterials. The combined approach is used to study the binding of gold nanoparticles to two types of phospholipid vesicles, those containing and lacking the model ion channel peptide gramicidin A. This model system serves as both a proof of concept for the method and a demonstration of the utility of the approach in studying nano-bio interactions. Two diffusional models (Stokes–Einstein and Kirkwood–Riseman) were compared in the determination of particle size, extent of binding, and nanoparticle:vesicle binding ratios for each vesicle type. The combination of NTA and statistical mixture distributions is shown to be a useful method for quantitative assessment of the extent of binding between particles and determination of binding ratios.

Mixture distribution and multifractal analysis applied to wind speed in the Brazilian Northeast region

Abstract The growing investments and installations of wind farms in the Brazilian Northeast have drawn attention to the region, leading investors and researchers to seek better ways of using the local wind regimen for energy production. In face of the complex behavior of wind speed time series, mixture distribution models have been applied to bimodal databases aiming at achieving the best modeling for series fitting. This paper used data from stations located in the nine states that make up the Brazilian Northeast region (Maranhao, Piaui, Ceara, Rio Grande do Norte, Paraiba, Pernambuco, Alagoas, Sergipe, and Bahia) between January 1st, 2004 and August 29th, 2018. The two-component Weibull distribution model was employed to model the historical series using the Expectation Maximization (EM) algorithm to search for optimal parameters in data distribution. Multifractal detrended fluctuation analysis was applied to verify series persistence over time and, using spatialization obtained with inverse distance weighting, the results were estimated at the sites lacking meteorological wind information. The results obtained indicate that the highest mean wind speeds are found in the states of Rio Grande do Norte, Paraiba, and Pernambuco, whereas the lowest occur in parts of Bahia, Piaui, and Maranhao. The highest mean wind speeds were recorded between 10 a.m. and 8 p.m. of each day at every station. Multifractal analysis revealed that wind speed series exhibit persistent overall behavior for all stations, with multifractality dominated by small fluctuations. For most of the stations both long term correlations and broad probability density function of wind speed values are found to cause multifractality of the process. This study allows identifying favorable areas for the installation of wind farms in different locations of the Brazilian Northeast region.

Fuzzy model identification based on mixture distribution analysis for bearings remaining useful life estimation using small training data set

The research work presented in this paper proposes a data-driven modeling method for bearings remaining useful life estimation based on Takagi-Sugeno (T-S) fuzzy inference system (FIS). This method allows identifying the parameters of a classic T-S FIS, starting with a small quantity of data. In this work, we used the vibration signals data from a small number of bearings over an entire period of run-to-failure. The FIS model inputs are features extracted from the vibration signals data observed periodically on the training bearings. The number of rules and the input parameters of each rule of the FIS model are identified using the subtractive clustering method. Furthermore, we propose to use the maximum likelihood method of mixture distribution analysis to calculate the parameters of clusters on the time axis and the probability corresponding to rules on degradation stages. Based on this result, we identified the output parameters of each rule using a weighted least square estimation. We then benchmarked the proposed method with some existing methods from the literature, through numerical experiments conducted on available datasets to highlight its effectiveness.

Skeletal Muscle Gene Expression in Long-Term Endurance and Resistance Trained Elderly.

Physical exercise is deemed the most efficient way of counteracting the age-related decline of skeletal muscle. Here we report a transcriptional study by next-generation sequencing of vastus lateralis biopsies from elderly with a life-long high-level training practice (n = 9) and from age-matched sedentary subjects (n = 5). Unsupervised mixture distribution analysis was able to correctly categorize trained and untrained subjects, whereas it failed to discriminate between individuals who underwent a prevalent endurance (n = 5) or a prevalent resistance (n = 4) training, thus showing that the training mode was not relevant for sarcopenia prevention. KEGG analysis of transcripts showed that physical exercise affected a high number of metabolic and signaling pathways, in particular those related to energy handling and mitochondrial biogenesis, where AMPK and AKT-mTOR signaling pathways are both active and balance each other, concurring to the establishment of an insulin-sensitive phenotype and to the maintenance of a functional muscle mass. Other pathways affected by exercise training increased the efficiency of the proteostatic mechanisms, consolidated the cytoskeletal organization, lowered the inflammation level, and contrasted cellular senescence. This study on extraordinary individuals who trained at high level for at least thirty years suggests that aging processes and exercise training travel the same paths in the opposite direction.

Novel insights into serodiagnosis and epidemiology of Erysipelothrix rhusiopathiae, a newly recognized pathogen in muskoxen (Ovibos moschatus).

Muskoxen are a key species of Arctic ecosystems and are important for food security and socio-economic well-being of many Indigenous communities in the Arctic and Subarctic. Between 2009 and 2014, the bacterium Erysipelothrix rhusiopathiae was isolated for the first time in this species in association with multiple mortality events in Canada and Alaska, raising questions regarding the spatiotemporal occurrence of the pathogen and its potential impact on muskox populations. We adapted a commercial porcine E. rhusiopathiae enzyme-linked immunosorbent assay to test 958 blood samples that were collected from muskoxen from seven regions in Alaska and the Canadian Arctic between 1976 and 2017. The cut-off between negative and positive results was established using mixture-distribution analysis, a data-driven approach. Based on 818 samples for which a serological status could be determined and with complete information, we calculated trends in sample seroprevalences in population time-series and compared them with population trends in the investigated regions. Overall, 219/818 (27.8%, 95% Confidence Interval: 24.7-31.0) samples were classified as positive for exposure to E. rhusiopathiae. There were large variations between years and regions. Seropositive animals were found among the earliest serum samples tested; 1976 in Alaska and 1991 in Canada. In Alaskan muskoxen, sample seroprevalence increased after 2000 and, in two regions, peak seroprevalences occurred simultaneously with population declines. In one of these regions, concurrent unusual mortalities were observed and E. rhusiopathiae was isolated from muskox carcasses. In Canada, there was an increase in sample seroprevalence in two muskox populations following known mortality events that had been attributed to E. rhusiopathiae. Our results indicate widespread exposure of muskoxen to E. rhusiopathiae in western Canada and Alaska. Although not new to the Arctic, we documented an increased exposure to the pathogen in several regions concurrent with population declines. Understanding causes for the apparent increased occurrence of this pathogen and its association with large scale mortality events for muskoxen is critical to evaluate the implications for wildlife and wildlife-dependent human populations in the Arctic.

Three-dimensional CFD analysis of hydrogen-air-steam explosions in APR1400 containment

The present study concerns the three-dimensional CFD analysis of hydrogen explosions in APR1400 containment. Initial conditions for combustion simulations are obtained by a cost-effective coupling with a lumped parameter code for preceding mixture distribution analysis. Three severe accident scenarios are examined: Small-Break Loss-Of-Coolant Accident (SB-LOCA) and Station Black-Out (SBO) with activated as well as deactivated three-way valve. Only in the last case, thermal ignition of the hydrogen-air-steam mixture could be triggered. Flame propagation in the containment and particularly in the In-containment Refueling Water Storage Tank (IRWST) is investigated in detail. Additional generic scenarios demonstrate the methods ability to reproduce strong Flame Acceleration (FA) and even the hazardous Deflagration-to-Detonation Transition (DDT).

Controlling Misclassification Rates in Identification of Haploid Seeds from Induction Crosses in Maize with High‐Oil Inducers

ABSTRACTIn vivo production of double haploid (DH) lines in maize (Zea mays L.) requires reliable identification of haploid (H) seeds. A new method for achieving this goal is production of induction crosses with high‐oil (HO) inducers and sorting the resulting H and diploid crossing (C) seeds based on their oil content (OC). Balancing the false discovery rate (FDR) and false negative rate (FNR) by choice of a suitable proportion α of selected seeds represents an unsolved problem with this method. We investigated solutions by applying mixture distribution (MD) analysis to the OC of induction crosses for estimating the means and standard deviation (μH, μC, and σ) of H and C seeds and the haploid induction rate κ. Moreover, we developed formulas and software for calculating the FDR and FNR from these estimates. Using several induction crosses with HO inducer UH600, parameter estimates from (i) MD analysis in different environments and (ii) gold standard classification (GSC) of plants in the field agreed well for μH and μC, but only moderately for σ and κ. Parameter estimates from the MD provided meaningful guidelines for calculating the expected FDR and FNR. Selecting the α = 7.5% proportion of seeds with lowest OC was optimal for most induction crosses and balanced the FDR and FNR. In conclusion, induction crosses with HO inducers hold great promise for promoting the DH technology in maize, but an automated high‐throughput platform for sorting the seeds from the MD into several distinct classes with increasing OC is recommended to take full advantage of this novel approach.

Gaussian Mixture Distribution Analysis as Estimation of Probability Density Function and it's the Periphery

In statistics, Mixture distribution model is a stochastic model for a measured data set to express existence of the subpopulation in a population, without requiring that the subpopulation to whom each observational data belongs should be identified. Formally, Mixture distribution model is equivalent to expressing the probability distributions of observational data in a population. However, it is although it is related to the problem relevant to Mixture distribution pulling out a population's characteristic out of subpopulation. Mixture distribution model is used without subpopulation's identity information in order to make the statistical inference about the characteristic of the subpopulation who was able to give only the observational data about a population simultaneously. This paper considered these matters from the similarity of the linear combination of an element function with estimation problem of a density function which used the Kernel function, and estimation problem of the density function using a Spline function. How to take Translate in arrangement of knots of estimation problem of the density function using the method of Bandwidth picking in estimation problem of the density function using a Kernel function and a Spline function and Wavelets analysis and Scale has a related thing.

Direction information in multiple object tracking is limited by a graded resource

Is multiple object tracking (MOT) limited by a fixed set of structures (slots), a limited but divisible resource, or both? Here, we answer this question by measuring the precision of the direction representation for tracked targets. The signature of a limited resource is a decrease in precision as the square root of the tracking load. The signature of fixed slots is a fixed precision. Hybrid models predict a rapid decrease to asymptotic precision. In two experiments, observers tracked moving disks and reported target motion direction by adjusting a probe arrow. We derived the precision of representation of correctly tracked targets using a mixture distribution analysis. Precision declined with target load according to the square-root law up to six targets. This finding is inconsistent with both pure and hybrid slot models. Instead, directional information in MOT appears to be limited by a continuously divisible resource.

Using Gaze-tracking Data and Mixture Distribution Analysis to Support a Holistic Model for the Detection of Cancers on Mammograms

Use data collected independently at three institutions to compare time to first fixate the true lesion in searching for cancers on mammograms. Examine the fit of the results to a holistic model of visual perception. The time required to first fixate a cancer on a mammogram was extracted from 400 eye-tracking records collected independently from three institutions. The time was used as an indicator of the initial perception of cancer. The distribution of first fixation times was partitioned into two normally distributed components using mixture distribution analysis. The true-positive fraction of each component was calculated. About 57% of the cancers had a 95% chance of being fixated in the first second of viewing. The remainder took longer (range, 1.0 to 15.2 seconds). The true-positive fraction was larger for the lesions hit immediately for most of the readers (TPF = 0.63 vs. 0.52, F = 5.88, P = .02) in 68% (13/19) of the readers. The initial detection occurs before visual scanning and, therefore, must be the result of a parallel "global" analysis of the image resulting in an initial holistic, gestalt-like perception. The development of expertise in medical image analysis may consist of a shift in the recognition mechanism from scan-look-detect to look-detect-scan.

Finite mixtures of MaxEnt distributions

Mixture distribution analysis has been the subject of a large remarkable diverse body of literature. So, in order to obtain a mixture density, the problem of parameter estimation has arisen and has taken an important role in this analysis. Parameter estimation is required not only for the parameters of the mixture component but also for the mixture proportion. Widely used method for this problem has been maximum likelihood whereas there are a number of specialized procedures such as least-squares criterion, graphical procedure, etc. In this study, in order to model mixture density, mixture of MaxEnt distributions is proposed instead of mixture of familiar distributions. Since MaxEnt distributions are non-parametric distributions, the problem is reduced to parameter estimation only for mixture proportion. Then, maximum equality estimator which also is based on Shannon’s entropy measure is proposed to be used. It is proved that the mixture of MaxEnt distributions is identifiable and gives more accurate fitting values rather than the mixture of familiar distributions without constructing the likelihood function.

Risk Factors for the Presence of High-Level Shedders ofEscherichia coliO157 on Scottish Farms

Escherichia coli O157 infections are the cause of sporadic or epidemic cases of often bloody diarrhea that can progress to hemolytic uremic syndrome (HUS), a systematic microvascular syndrome with predominantly renal and neurological complications. HUS is responsible for most deaths associated with E. coli O157 infection. From March 2002 to February 2004, approximately 13,000 fecal pat samples from 481 farms with finishing/store cattle throughout Scotland were examined for the presence of E. coli O157. A total of 441 fecal pats from 91 farms tested positive for E. coli O157. From the positive samples, a point estimate for high-level shedders was identified using mixture distribution analysis on counts of E. coli O157. Models were developed based on the confidence interval surrounding this point estimate (high-level shedder, greater than 10(3) or greater than 10(4) CFU g(-1) feces). The mean prevalence on high-level-shedding farms was higher than that on low-level-shedding farms. The presence of a high-level shedder on a farm was found to be associated with a high proportion of low-level shedding, consistent with the possibility of a higher level of transmission. Analysis of risk factors associated with the presence of a high-level shedder on a farm suggested the importance of the pathogen and individual host rather than the farm environment. The proportion of high-level shedders of phage 21/28 was higher than expected by chance. Management-related risk factors that were identified included the type of cattle (female breeding cattle) and cattle stress (movement and weaning), as opposed to environmental factors, such as water supply and feed.

Bayesian finite mixtures with an unknown number of components: The allocation sampler

A new Markov chain Monte Carlo method for the Bayesian analysis of finite mixture distributions with an unknown number of components is presented. The sampler is characterized by a state space consisting only of the number of components and the latent allocation variables. Its main advantage is that it can be used, with minimal changes, for mixtures of components from any parametric family, under the assumption that the component parameters can be integrated out of the model analytically. Artificial and real data sets are used to illustrate the method and mixtures of univariate and of multivariate normals are explicitly considered. The problem of label switching, when parameter inference is of interest, is addressed in a post-processing stage.

Characterizing in vitro hippocampal ripples using time–frequency analysis

We analyze in vitro hippocampal activity exhibiting drug induced ripple-like rhythms using time–frequency distributions. The different tradeoffs between time–frequency resolution, interference, and range are examined with reference to the suitability of each for use in analyzing ripple data. An unbiased approach is taken to characterizing ripple rhythms uniquely by determining the parameter choices in which its behaviour is most distinct from baseline activity. Mixture distribution analysis of the two components generated from correlating frequency behaviour allows a clear method for determining the distinctiveness of ripple-like rhythms given a particular parameter choice.

FUZZY CLASS LOGISTIC REGRESSION ANALYSIS

Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

Finite Mixture Analysis of Beauty-Contest Data from Multiple Samples

This paper develops a finite mixture distribution analysis of Beauty-Contest data obtained from diverse groups of experiments. ML estimation using the EM approach provides estimates for the means and variances of the component distributions, which are common to all the groups, and estimates of the mixing proportions, which are specific to each group. This estimation is performed without imposing constraints on the parameters of the composing distributions. The statistical analysis indicates that many individuals follow a common pattern of reasoning described as iterated best reply (degenerate), and shows that the proportions of people thinking at different levels of depth vary across groups.

Mixture distribution analysis of a computer assisted diagnostic method for the evaluation of pulmonary nodules on computed tomography scan 1

Rationale and objectives To compare the effectiveness of a new computational scheme for pulmonary nodule detection in computed tomography images against human observers. Materials and methods The study involved evaluation of 81 potential nodules by four radiologists. Each radiologist separately evaluated the potential nodules and provided a confidence level for the presence of pulmonary nodules. Their performance was compared with that of the new computational scheme by mixture distribution analysis. Results Mixture distribution analysis of the results of the four radiologists demonstrated a relative proportion agreement of 0.84. The kappa statistic was used to compare the agreement of the computational scheme with the results of the four radiologists. A kappa value of .65 (se = .11) was shown to be significantly different from chance ( P = .99). Conclusion The new computational scheme correlates well with the radiologists’ subjective rankings of pulmonary nodules on computed tomography scans and may prove a useful tool in the evaluation of algorithms for the screening and diagnosis of lung cancer.

Mixture distribution analysis of phenotypic markers reflectingHFEgene mutations

AbstractThe goal of this study was to determine whether statistical modeling of population data for a phenotypic marker could reflect a major locus gene defect. Identifying mutations in theHFEgene makes it possible to assess the association between transferrin saturation (TS) subpopulations andHFEmutations. Data were analyzed from 27 895 white patients who attended a health appraisal clinic and who had TS and common mutations ofHFEdetermined. Mixture distribution modeling of TS was performed, and the proportion ofHFEmutations in TS subpopulations was assessed on a probability basis. Three subpopulations of TS were identified, consistent with Hardy-Weinberg conditions for major locus effects. For men, 72% of the subpopulation with the highest mean TS hadHFEgene mutations; they were primarily homozygotes or compound heterozygotes. Seventy-three percent of the subpopulation with moderate mean TS also hadHFEgene mutations; they were predominantly simple heterozygotes. Sixty-seven percent of the subpopulation with the lowest mean TS were wild-type homozygotes. Similar results were observed for women. These results suggest that statistical modeling of population clinical laboratory test data can reveal the influence of a major locus gene defect and perhaps can be applied to other aspects of body metabolism than iron. (Blood. 2003;102:4563-4566)

Population dynamics of the sympagic amphipods Gammarus wilkitzkii and Apherusa glacialis in sea ice north of Svalbard

The population structure and production of the two autochthonous sympagic amphipods, Gammarus wilkitzkii and Apherusa glacialis, collected in different categories of sea ice north of Svalbard and in the Fram Strait, were examined. A longevity of 6 years for male G. wilkitzkii and 5–6 years for females was indicated, using a Mixture distribution analysis technique. Growth is best described by the Gompertz growth function. The theoretical maximum body length was estimated to be 53.2 and 45.3 mm, and the corresponding maximum age was estimated to be 7.5 and 6.3 years for males and females, respectively. Juveniles of age classes 0+ and 1+ of G. wilkitzkii were most abundant in first-year ice and were regarded as predominant colonizers of new ice habitats. It is unclear whether juveniles have colonized the ice independently or been released there by females colonizing the new ice. Age classes 2+ and 3+ were numerous in multi-year ice. The growth rate for G. wilkitzkii was low, and lower for females than for males. Highest growth rates were found in an area dominated by old ice. A mean production of 0.0237 g ash-free dry weight year–1 m–2 and a somatic P/B ratio (productivity) of 0.255 year–1 were calculated for the entire set of data. Individuals of age class 4+ were the most productive within the population, while juveniles have little influence on the annual productivity. A. glacialis reached a maximum age of 2 years and age class 0+ was about tenfold more abundant compared to age class 1+, indicating a high mortality rate during the 1st year of life. The population structure seems to be more affected by ice conditions (e.g. floe size) than by the age of the ice.