Mixture Distribution Model Research Articles

Modeling the minus two base pair stutter ratio of the D1S1656 locus: A sequence-based mixture distribution model

In this study, we propose a stutter ratio for a minus two base pair stutter (-2bpSR) model of the D1S1656 locus in capillary electrophoresis (CE)-based short tandem repeat (STR) typing. DNA from a total of 108 Japanese individuals was analyzed via massively parallel sequencing to investigate the length of the longest uninterrupted stretch of two base repeat motif (2bpLUS value) within repetitive structures involving the flanking region. Additionally, -2bpSR data was collected using the GlobalFiler Kit on a 3500xL Genetic Analyzer. As a result of sequencing analysis, all alleles were classified into two types by their 2bpLUS values. The -2bpSR differed significantly between the types. Then, we modeled the -2bpSR with a mixture log-normal distribution using the classification of alleles based on the 2bpLUS values. Furthermore, probabilities of the sequence type within each repeat number in the mixture log-normal distribution model were estimated using logistic regression for each of the five major detected populations. This study is expected to enable interpretation of STR typing while considering minus two base pair stutter at the D1S1656 locus.

A Mean Field Games model for finite mixtures of Bernoulli and categorical distributions

Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the Expectation-Maximization algorithm. We propose an alternative approach based on the theory of Mean Field Games, a class of differential games with an infinite number of agents. We show that the solution of a finite state space multi-population Mean Field Games system characterizes the critical points of the log-likelihood functional for a Bernoulli mixture. The approach is then generalized to mixture models of categorical distributions. Hence, the Mean Field Games approach provides a method to compute the parameters of the mixture model, and we show its application to some standard examples in cluster analysis.

A Novel Scenario Generation Framework Based on the Knowledge of Existing Wind Power Plants

As a kind of renewable energy with economic and environmental friendliness, wind energy is widely used, although the high uncertainty of wind speed has significant impact on the operation and planning of wind power systems. Thus, scenario generation of wind speed is the primary step to obtain optimal decisions. However, as to the wind power plants to be newly-built or expanded, adequate wind data may not be available, or even the wind data are missing or invalid, which may lead to the inaccuracy of data-driven scenario generation. In this paper, considering that multiple wind plants in neighboring areas may have similar wind patterns, a novel scenario generation framework is proposed to transfer the knowledge extracted from existing data-rich plants to help establish the uncertainty model of newly-built plant. Transfer component analysis (TCA) is used to minimize the distribution gap between multiple source plants and target plant, and the results of maximum mean discrepancy (MMD) can be obtained to construct the mixture distribution model of target wind speed. Experimental results show that the scenarios generated by transferring the knowledge of existing wind plants can better reflect the real characteristics of the target wind speed in the case of insufficient historical data.

Very short term load forecasting of residential electricity consumption using the Markov-chain mixture distribution (MCM) model

This study utilizes the Markov-chain mixture distribution model (MCM) for very short term load forecasting of residential electricity consumption. The model is used to forecast one step ahead half hour resolution residential electricity consumption data from Australia. The results are compared with Quantile Regression (QR) and Persistence Ensemble (PeEn) as advanced and simple benchmark models. The results were compared in terms of reliability, reliability mean absolute error (rMAE), prediction interval normalized average width (PINAW) and normalized continuous ranked probability score (nCRPS). For 10 steps conditioning for QR and PeEn, the MCM results were on par with QR, and superior to PeEn. As a sensitivity analysis, simulations were performed where the number of data points for conditioning QR and PeEn was varied and compared to the MCM output, which is based on only one data point for conditioning. It was shown that in terms of nCRPS and rMAE the QR results converged towards the MCM results for lower number of conditioning points included in QR. The nCRPS of PeEn never reached the superior MCM and QR results, but in rMAE, for number of conditioning points above 24, PeEn was the most reliable. Based on the sparse complexity design of MCM, high computational speed and competitive performance, it is suggested as a candidate for benchmark model in probabilistic forecasting of electricity consumption.

Mutation Profiles Identify Distinct Clusters of Lower Risk Myelodysplastic Syndromes with Unique Clinical and Biological Features and Clinical Endpoints

Mutation Profiles Identify Distinct Clusters of Lower Risk Myelodysplastic Syndromes with Unique Clinical and Biological Features and Clinical Endpoints

Public acceptance of Covid-19 lockdown scenarios.

By mid-March 2020, most countries had implemented nationwide lockdown policies aimed at decelerating the spread of SARS-CoV-2. At that time, nobody knew how long these policies would have to remain in force and whether they would have to be extended, intensified or made more flexible. The present study aimed to illuminate how the general public in Germany reacted to the prospect of increasing the length, the intensity and/or the flexibility of distancing rules implied by different lockdown scenarios. Endorsement of and compliance with five specific lockdown scenarios were assessed in a large (N=14,433) German sample. Results showed that lockdown length affected respondents' reactions much more strongly than intensity or flexibility. Additional analyses (i.e., mixture distribution modelling) showed that half of the respondents rejected any further extensions or intensifications, while 20% would endorse long-term strategies if necessary. We argue that policy-makers and political communicators should take the public's endorsement of and compliance with such scenarios into account, as should simulations predicting the effects of different lockdown scenarios.

An Objective Method for Probabilistic Forecasting of Multimodal Kuroshio States using Ensemble Simulation and Machine Learning

AbstractThis paper presents a method for detecting the ensemble means, spreads, and occurrence probabilities for each of the multiple Kuroshio states. This is accomplished by classifying the forecasts of the ensemble members with a Gaussian mixture distribution model, a machine learning method. Ensemble simulations with 80 members are conducted to reproduce possible occurrences of the multiple Kuroshio states, targeting the large meander event in 2017. To test its performance, first, the method is applied for the southernmost latitude, a conventional index that represents meander intensity. The results show that the Kuroshio initially taking the nearshore nonlarge meander state bifurcates into the large meander and offshore nonlarge meander states, which occur with similar probabilities. Both developments are accompanied by positive potential energy extraction rates, consistent with baroclinic instability. As a more objective approach, the method is then applied for the dominant modes derived from empirical orthogonal function (EOF) analysis of the sea surface height field in the entire Kuroshio region. Importantly, almost identical results can be achieved. In particular, the bimodality between the large meander and nonlarge meander is shown to appear on the axis of the first EOF mode. From a mathematical perspective, this mode can be interpreted as the singular vector which grows most rapidly following the time-evolution operator. Finally, the multimodality of the Kuroshio is reinterpreted as a phase transition phenomenon where the nearshore nonlarge meander constitutes the basic state.

Regularized matrix data clustering and its application to image analysis

We propose a novel regularized mixture model for clustering matrix-valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (eg, low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix-normal distributions with regularization terms, and then develop an expectation maximization type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of thesolution.

Cotton thrips infestation predictor: a practical tool for predicting tobacco thrips (Frankliniella fusca) infestation of cotton seedlings in the south-eastern United States.

Thrips (order Thysanoptera) infestations of cotton seedlings result in plant injury, increasing the detrimental consequences of other challenges to production agriculture, such as abiotic stress or infestation by other pests. Using Frankliniella fusca as a thrips species of focus, we empirically developed a composite model of thrips phenology and cotton seedling susceptibility to predict site-specific infestation risk so that monitoring and other resources can be allocated efficiently, to optimize the timing of thrips control measures to maximize effectiveness, and to inform stakeholders about the dynamics of thrips infestation and cotton seedling injury at a time when thrips are evolving resistance to commonly-used pesticides. A mixture distribution model of thrips infestation potential, fit to data describing F. fusca adult dispersal in time, proved best for predicting infestations of F. fusca on cotton seedlings. Thrips generations occurring each year as a function of weather are represented as a probability distribution. A model of cotton seedling growth was also developed to predict susceptibility as a function of weather. Combining these two models resulted in a model of seedling injury, which was validated and developed for implementation as a software tool. Experimental validation of the implemented model demonstrated the utility of its output in predicting infestation risk. Successful implementation and use of the software tool derived from this model was enabled by close cooperation with university extension personnel, agricultural consultants, and growers, underscoring the importance of stakeholder and expert input to the success of applied analytical research. © 2020 Society of Chemical Industry.

Rényi Entropy for Mixture Model of Multivariate Skew Laplace distributions

Rényi entropy is an important concept developed by Rényi in information theory. In this paper, we study in detail this measure of information in cases multivariate skew Laplace distributions then we extend this study to the class of mixture model of multivariate skew Laplace distributions. The upper and lower bounds of Rényi entropy of mixture model are determined. In addition, an asymptotic expression for Rényi entropy is given by the approximation. Finally, we give a real data example to illustrate the behavior of entropy of the mixture model under consideration.

Student Mixture and Its Machine Learning Applications to PVT Properties of Reservoir Fluids

Distribution mixture models are widely used in cluster analysis. Particularly, a mixture of Student t-distributions is mostly applied for robust data clustering. In this paper, we introduce EM algorithm for a mixture of Student distributions, where at the E-step, we apply variational Bayesian inference for parameters estimation. Based on a mixture of Student distributions, a machine learning method is constructed that allows solving regression problems for any set of features, clustering, and anomaly detection within one model. Each of these problems can be solved by the model even if there are missing values in the data. The proposed method was tested on real data describing the PVT properties of reservoir fluids. The results obtained by the model do not contradict the basic physical properties. In majority of conducted experiments our model gives more accurate results than well-known machine learning methods in terms of MAPE and RMSPE metrics.

Mixture distribution modeling for scalable graph-based semi-supervised learning

Graph-based semi-supervised learning (SSL) has been widely investigated in recent works considering its powerful ability to naturally incorporate the diverse types of information and measurements. However, traditional graph-based SSL methods have cubic complexities and leading to low scalability. In this paper, we propose to perform graph-based SSL on mixture distribution components, named Mixture-distribution based Graph Smoothing (MGS), to address this challenge. Specifically, the intrinsic distributions of data are captured by a mixture density estimation model. A novel mixture-distribution based objective energy function is further proposed to incorporate few available annotations, which ensures the model complexity is irrelevant to the number of raw instances. The energy function can be simplified and effectively solved by viewing the instances and mixture components as the point clouds. Experiments on large datasets demonstrate the remarkable performance improvements and scalability of the proposed model, which proves the superiority of the MGS model.

Integrated assessment of the spatial distribution and structural dynamics of deep benthic marine communities.

Characterizing the spatial distribution and variation of species communities and validating these characteristics with data from the field are key elements for an ecosystem-based approach to management. However, models of species distributions that yield community structure are usually not linked to models of community dynamics, constraining understanding and management of the ecosystem, particularly in data-poor regions. Here we use a qualitative network model to predict changes in Antarctic benthic community structure between major marine habitats characterized largely by seafloor depth and slope, and use multivariate mixture models of species distributions to validate the community dynamics. We then assess how future increases in primary production associated with anticipated loss of sea-ice may affect the ecosystem. Our study shows how both spatial and structural features of ecosystems in data-poor regions can be analyzed and possible futures assessed, with direct relevance for ecosystem-based management.

Determination of Wind Potential by Two Components Mixture Probability Distribution Models in the Ankara, TURKEY

In this study, hourly average wind speed data in the Ankara, Turkey are modeled with Weibull, Gamma and Rayleigh probability distribution and theirs two component mixture probability distributions. Expectation-Maximization (EM) algorithm is introduced for Maximum Likelihood Estimation (MLE) of mixture probability distributions used in modeling wind speed data. In comparing the modeling performances of probability distributions, the Akaike information criteria ( ), the coefficient of determination ( ), the root of the mean squares ( ) and chi-square ( ) criteria were used as comparison criteria. Also, in this study, the success in estimation of wind potential was evaluated with relative error. In the study results, it was observed that the mixture distribution models obtained from two different distributions were more successful in modeling wind speed data.

Robust Feature-Based Point Registration Using Directional Mixture Model

Abstract This paper presents a robust probabilistic point registration method for estimating the rigid transformation (i.e. rotation matrix and translation vector) between two pointcloud dataset. The method improves the robustness of point registration and consequently the robot localization in the presence of outliers in the pointclouds which always occurs due to occlusion, dynamic objects, and sensor errors. The framework models the point registration task based on directional statistics on a unit sphere. In particular, a Kent distribution mixture model is adopted and the process of point registration has been carried out in the two phases of Expectation-Maximization algorithm. The proposed method has been evaluated on the pointcloud dataset from LiDAR sensors in an indoor environment.

Estimation of finite mixture models of skew-symmetric circular distributions

Analysis of circular data is challenging, since the usual statistical methods are unsuitable and it is necessary to use circular periodic probabilistic models. Because some actual circular datasets exhibit asymmetry and/or multimodality, finite mixtures of symmetric circular distributions to model and fit these data have been investigated. However, it is necessary to question the predominant assumption that each component in the finite mixture model is symmetric. In this study, we consider a finite mixture model of possibly skewed circular distributions and discuss the expectation-maximization (EM) algorithm for the maximum likelihood estimate. It is shown that the maximum likelihood estimator is strongly consistent under some suitable conditions in a finite mixture of skew-symmetric circular distributions. A modified M-step in the EM algorithm is proposed in order to estimate the unknown parameter vectors effectively. To investigate the performance of our proposed model with its estimation procedure, we provide a numerical example as well as data analysis using the records of the time of day of fatal traffic accidents.

A REMARK ON L2 DISTANCE FUNCTION AND NON-IDENTIFIABILITY PROBLEM OF FINITE MIXTURE DISTRIBUTION MODELS IN MODEL-BASED CLASSIFICATION

Finite mixture models provide flexible method of modeling data obtained from population consisting of finite number of homogeneous subpopulations. One of the main areas in which the finite mixture model structures is practically used in statistics is model based classification. However, the result of non identifiability problem arising from the structure of the finite mixture models may cause unreliable results on classification. In this paper we compare the probability density functions ( ) of the finite mixture distribution models for two different populations by L2 distance. We propose the componentwise L2 distance function to compare the of finite mixture distribution models for two different populations in the presence of non identifiability problem. Besides, a condition is proposed to control whether the L2 distance function gives similar results with the componentwise L2 distance function to compare the of finite mixture distribution models for two different populations.

Probability distribution of wave periods in combined sea states with finite mixture models

The short-term distribution of wave periods is very important for ocean and coastal engineering applications. At present, the vast majority of research studies are confined to single-wave systems. Most available theoretical distributions of wave periods, which are based on the narrowband approximation, are inapplicable to actual sea states. This study focuses on the probability distribution of individual wave periods in combined sea states with two parametric mixture distribution models. The expectation-maximisation (EM) algorithm is used to calculate the maximum likelihood estimates of the mixture models. Further, the mixture distributions are compared with other two models: a theoretical and a parametric model. In situ-measured data with two-peaked spectra and simulated data obtained with the six-parameter Ochi–Hubble model allow for a thorough assessment of the distribution models. The patterns of the distributions of wave periods in nine types of mixed sea states are considered and discussed. According to the results, the theoretical distribution model is unsuitable for the description of the distributions in mixed sea states; in particular, when the patterns exhibit bimodal characters. By contrast, despite having a higher calculation complexity, the mixture distribution models provide an improved performance for all combined-sea state cases.

Combining mixture distribution and multidimensional IRTree models for the measurement of extreme response styles.

Personality constructs, attitudes and other non-cognitive variables are often measured using rating or Likert-type scales, which does not come without problems. Especially in low-stakes assessments, respondents may produce biased responses due to response styles (RS) that reduce the validity and comparability of the measurement. Detecting and correcting RS is not always straightforward because not all respondents show RS and the ones who do may not do so to the same extent or in the same direction. The present study proposes the combination of a multidimensional IRTree model with a mixture distribution item response theory model and illustrates the application of the approach using data from the Programme for the International Assessment of Adult Competencies (PIAAC). This joint approach allows for the differentiation between different latent classes of respondents who show different RS behaviours and respondents who show RS versus respondents who give (largely) unbiased responses. We illustrate the application of the approach by examining extreme RS and show how the resulting latent classes can be further examined using external variables and process data from computer-based assessments to develop a better understanding of response behaviour and RS.

Premium rate determination of crop insurance product based on rainfall index consideration

Crop insurance product based on rainfall index is an alternative product to minimize the risk in the agricultural sector. Rainfall index is supposed to represent crop failure in a specific area. Rainfall index is composed of parameters, trigger, and exit. The trigger is a benchmark value of rainfall that causes the partial risk and gives the right to the policyholder to begin partial benefit payment. The exit is the benchmark value of rainfall that consists of total crop failure and assigns the right to the policyholder to submit full benefit claim. The trigger and the exit in a rainfall index provide the value of the premium. A case study is carried out with cumulative rainfall data from June to August in the Dramaga area of Bogor from 1984 until 2017 to ensure paddy. The two-component Gamma Mixture distribution model is applied to determine the rate of premium that must be paid by the policyholder on the specified rainfall index.