Finite Mixture Research Articles

Copula-based JPDF of wind speed, wind direction, wind angle, and temperature with SHM data

Structural health monitoring (SHM) systems installed on long-span bridges can obtain environmental data around them. To deeply mine the correlation between types of data, this paper proposes a multivariant joint probability density distribution function (JPDF) based on copula theory. Specifically, the univariate probability density function (PDF) is characterized by the finite mixture (FM) method, that is, the 1D model. In addition, the parameters in the FM distribution are estimated by the genetic algorithm (GA). Then, the bivariate JPDF based on copula theory is established, i.e., the 2D model; next, the trivariate JPDF is derived, i.e., the 3D model. Furthermore, the quaternary JPDF of wind speed, wind direction, wind angle, and temperature is derived, i.e., the 4D model. The feasibility of the proposed model is verified by a case study of a specific bridge in China, on which the SHM system is installed to collect SHM data including wind speed, wind direction, wind angle, and temperature. The trivariate JPDF of wind speed, wind direction, and wind angle, and the trivariate JPDF of wind speed, wind direction, and temperature based on FM are established.

Mixture regression modelling based on the shape mixtures of skew Laplace normal distribution

Modelling skewness and heavy-tailedness in heterogeneous data sets is a compelling problem, particularly in regression analysis. The main goal of this study is to propose a mixture regression model based on the shape mixtures of skew Laplace normal (SMSLN) distribution for modelling skewness and heavy-tailedness simultaneously. The SMSLN distribution has been introduced by Doğru and Arslan [Finite mixtures of skew Laplace normal distributions with random skewness. 11th International Statistics Congress (ISC2019); Bodrum/Turkey; Finite mixtures of skew Laplace normal distributions with random skewness. Comput Stat. 2021;36(1):423–447] as a flexible extension of the skew Laplace normal (SLN) distribution and includes an extra shape parameter that controls skewness and kurtosis. The maximum likelihood estimators for the parameters of interest with the help of the expectation-maximization (EM) algorithm are obtained. The performance of the proposed mixture model is demonstrated via a simulation study and a real data example.

A General Mixture Model for Cognitive Diagnosis

Although the generalized deterministic inputs, noisy “and” gate model (G-DINA; de la Torre, 2011) is a general cognitive diagnosis model (CDM), it does not account for the heterogeneity that is rooted from the existing latent groups in the population of examinees. To address this, this study proposes the mixture G-DINA model, a CDM that incorporates the G-DINA model within the finite mixture modeling framework. An expectation–maximization algorithm is developed to estimate the mixture G-DINA model. To determine the viability of the proposed model, an extensive simulation study is conducted to examine the parameter recovery performance, model fit, and correct classification rates. Responses to a reading comprehension assessment were analyzed to further demonstrate the capability of the proposed model.

Motives behind cooperation in finitely repeated prisoner's dilemma

This paper deploys a novel experiment to compare three behavioral theories that explain both selfish and non-selfish cooperation. The three theories fuse reputational cooperation (à la Kreps et al. (1982)) with the following three non-selfish motives respectively: caring about others (Altruism), being conscientious about cooperation (Duty), and enjoying social-efficiency (Efficiency-Seeking). We use reputational cooperation under purely Selfish preferences as a fourth theory. Our experimental design varies the decline-rate of future rewards, under which these theories predict rich patterns of behavior. Based on a Finite Mixture Model, the data is best explained if the modal subject types are Selfish and Efficiency-Seeking: We estimate that 40-49% of our subjects are Selfish, 36-45% are Efficiency-seeking, and 6-20% are Altruistic. We find little evidence for Duty players.

Identification of mixtures of dynamic discrete choices

This paper provides new identification results for finite mixtures of Markov processes. Our arguments yield identification from knowledge of the cross-sectional distribution of three (or more) effective time-series observations under simple conditions. We explain how our approach and results are different from those in previous work by Kasahara and Shimotsu (2009) and Hu and Shum (2012). Most notably, outside information, such as monotonicity restrictions that link conditional distributions to latent types, is not needed.

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.

Multivariate mix-GEE models for longitudinal data with multiple outcomes

Multivariate longitudinal studies often involve two or more outcomes of interest measured repeatedly across time for each subject. A main challenge in the analysis of such data is the complex correlation structure. Appropriate modeling of the covariance matrix can provide more efficient parameter estimators. In this paper, multivariate finite mixture models are built for the working correlation matrix of the generalized estimating equations (GEE). A new procedure is proposed to estimate the parameters while ensuring the positive definiteness of the estimated working correlation matrix. Moreover, the consistency and the asymptotic normality of the parameter estimates are derived theoretically. Furthermore, if data are from a Gaussian mixture model, the estimators can be proved to be asymptotically efficient. In addition, the proposed method is illustrated through several simulation studies and a real data example of transportation safety.

Extropy: Characterizations and dynamic versions

AbstractSeveral information measures have been proposed and studied in the literature. One such measure is extropy, a complementary dual function of entropy. Its meaning and related aging notions have not yet been studied in great detail. In this paper, we first illustrate that extropy information ranks the uniformity of a wide array of absolutely continuous families. We then discuss several theoretical merits of extropy. We also provide a closed-form expression of it for finite mixture distributions. Finally, the dynamic versions of extropy are also discussed, specifically the residual extropy and past extropy measures.

Hierarchical Deep Reinforcement Learning for Self-Powered Monitoring and Communication Integrated System in High-Speed Railway Networks

To align with the vision of future intelligent high-speed railway (HSR) networks, integrating sensor monitoring and remote communication are challenging for ensuring the lightweight of train equipment, high-quality transmissions, and dynamic interaction between monitoring and communication. In this paper, we propose a self-powered multisensor monitoring and communication integrated system in HSR. A low-power backscatter communication working framework of the self-powered monitoring system is designed in the monitoring network model, and a finite Gaussian mixture model (GMM) clustering method is used to analyze the communication cell coverage area in the communication network model. Aiming to minimize the total task completion time, we formulate a data monitoring and remote communication problem with the energy transfer constraint, data collection constraint, and transmission data rate constraint. As for the non-convex minimum time optimization problem, we develop a novel option-based hierarchical deep reinforcement learning (OHDRL) method to deal with the complex continuous variation characteristics of the monitoring and communication integrated HSR system. The system learns to select options at a high level, and the action is executed according to the policy of the selected option at a low level. This approach enables us to handle stochastic HSR environments, closed-loop policies, and goals in a temporal abstraction way. Numerical results reveal that the proposed algorithm for the integrated monitoring and communication HSR achieves a significantly higher reward and more stable learning performance than other algorithms in the literature.

Antidepressant adherence trajectory before cancer diagnosis and risk of antidepressant discontinuation after cancer diagnosis among middle-aged US adults.

e18890 Background: For middle-aged adults taking antidepressants before cancer diagnosis, concerns exist about drug-drug interactions between antidepressants and antineoplastics. Clinical guidelines recommend detailed assessment of the new cancer survivor's past history of antidepressant use before considering antidepressant discontinuation. We aimed to determine whether, in real-world settings, the risk of antidepressant discontinuation after cancer diagnosis is associated with survivors’ past antidepressant adherence trajectories. Methods: A retrospective cohort of 45 to 64-year old individuals with incident cancer diagnosis (index date) and ≥2 antidepressant fills in the 9 months before index date, IQVIA PharMetrics Plus for Academics claims, 2006-2020. Antidepressant adherence in the 9-month baseline was measured as monthly proportion of days covered (PDC) before tamoxifen initiation. Group-based trajectory modeling (GBTM) was used to identify clusters of survivors with distinct antidepressant adherence trajectories pre-index date i.e., we calculated polynomial functions of monthly PDCs and compared 2 to 6-group finite mixture models to determine which model best fit the data, based on the Bayesian Information Criterion, expert-adjudged parsimony and ≥10% of the sample in each trajectory group. Antidepressant discontinuation after cancer diagnosis was defined as a 45-day gap in antidepressant supply. Survivors were censored at first of either antidepressant discontinuation, loss of enrollment or 1 year post-index date. Cox regression compared the hazard of antidepressant discontinuation by trajectory group, adjusted for demographics, mental disorder and cancer type. Results: We identified 7,293 middle-aged cancer survivors with prior antidepressant use; females 72%, mean age (SD) 56 (7) years. GBTM identified 4 adherence trajectory groups (consistently high, steady increase, declining, and recent start); metastatic cancer being characteristic of the latter 3 groups relative to the consistently high group. Antidepressant discontinuation was lowest in the consistently high group (26% [mean months-to-discontinuation: 9]) and highest in the declining (68% [5]) and recent start (51% [6]) groups, p < .01. Hazard ratios [95% CI] of discontinuation were significantly higher in the declining (2.7 [2.3 – 3.2]), recent start (1.9 [1.7 – 2.0]) and steady increase (1.5 [1.4 – 1.6]) groups, relative to the consistently high group. Conclusions: Middle-aged cancer survivors with past trajectories of consistently high adherence to antidepressants experience lower risk of antidepressant discontinuation after cancer diagnosis in real-world practice. However, concern remains about the unintended health outcomes of relatively higher antidepressant discontinuation among survivors diagnosed with metastatic cancer.

Clustering patients with vascular cognitive impairment using quantitative magnetic resonance imaging data and a finite mixture model

AbstractBackgroundBlood‐brain barrier (BBB) leakage is a marker of vascular cognitive impairment and dementia (VCID). The advance of in vivo imaging enabled us to quantify the degree of BBB transfer rates in VCID patients. However, a consensus has not been reached on the role of BBB in the differential diagnosis of VCI subtypes. The objective of this work was to use neuroinflammatory and in vivo imaging data on BBB health to identify clusters of VCID patients with distinct underlying pathologies.MethodPatients included were on average 61 (SD = 15.94, M/F = 27/34) years old. The MRI data were collected by using a 1.5 Tesla Siemens Sonata scanner. Pixel‐by‐pixel BBB transfer rate (Ki) was calculated using Patlak compartmental analysis on dynamic contrast‐enhanced T1 maps. The mean BBB transfer rate was calculated for the brain section above the ventricular zone (sampled by six consecutive slices). MR Spectroscopy was used to investigate N‐Acetylaspartate (NAA), Creatine (Cr), and Choline (Cho) levels. Moreover, Active MMP3 data were used in patients clustering. Thirty‐eight patients enrolled in the study have all data for three entities; NAA, mean Ki, and active MMP3 used for clustering. A multi‐parametric model‐based classification method was used to blindly classify VCID data based on Ki, NAA, and active MMPs.ResultBBB leakage increased by age, which is more pronounced in patients diagnosed with cognitive impairment when compared with 17 controls, r2 = 0.060, P = 0.021. Statistical classifiers identified three clusters in VCID patients. Identified VCID clusters are similar to the distinction that was made on this VCID cohort based on the clinical scores and psychological entities that we have published earlier.ConclusionThe results suggest that a statistical combination of imaging and inflammatory attributes renders a tool to blindly separate VCID patients into distinct groups that may have different underlying pathology.

Bayesian analysis for imbalanced positive-unlabelled diagnosis codes in electronic health records

With the increasing availability of electronic health records (EHR), significant progress has been made on developing predictive inference and algorithms by health data analysts and researchers. However, the EHR data are notoriously noisy due to missing and inaccurate inputs despite the information is abundant. One serious problem is that only a small portion of patients in the database has confirmatory diagnoses while many other patients remain undiagnosed because they did not comply with the recommended examinations. The phenomenon leads to a so-called positive-unlabelled situation and the labels are extremely imbalanced. In this paper, we propose a model-based approach to classify the unlabelled patients by using a Bayesian finite mixture model. We also discuss the label switching issue for the imbalanced data and propose a consensus Monte Carlo approach to address the imbalance issue and improve computational efficiency simultaneously. Simulation studies show that our proposed model-based approach outperforms existing positive-unlabelled learning algorithms. The proposed method is applied on the Cerner EHR for detecting diabetic retinopathy (DR) patients using laboratory measurements. With only 3% confirmatory diagnoses in the EHR database, we estimate the actual DR prevalence to be 25% which coincides with reported findings in the medical literature.

Mixture Based Superpixel Segmentation and Classification of SAR Images

Abstract: The proposed approach suggests a mixture-based super pixel segmentation technique for synthetic aperture radar (SAR) images. SAR is a radar system used to generate 2D or 3D representations of objects like landscapes. This method utilizes SAR image amplitudes and pixel coordinates as features. Super pixels are large irregular-shaped regions obtained through oversegmentation of an image. While super pixel segmentation methods are commonly designed for colour images, this approach adapts a finite mixture model (FMM) for single-channel SAR images. By employing finite mixture models, the pixels are clustered into super pixels. Following the super pixel segmentation, the method employs a hierarchical decision tree clustering algorithm for classifying different land covers, such as climate monitoring and natural resources exploitation. The decision tree algorithm creates a dendrogram or tree structure to group feature vectors. The proposed super pixel method demonstrates improved classification accuracy compared to state-of-the-art methods like quick-shift, turbo pixels, simple linear iterative clustering, and pixel intensity and location similarity. The implementation of the proposed method is efficiently carried out using MATLAB software.

Recursive Selection of Hyperexponential Distributions in Approximation of Distributions with "Heavy Tails"

It is known that many quantities that determine the network characteristics of the functioning of an infocommunication network have probability distributions with "heavy tails", which can have a significant impact on network performance. Models with heavy-tailed distributions tend to be difficult to analyze. The analysis can be simplified by using an algorithm to approximate a heavy-tailed distri-bution by a hyperexponential distribution (a finite mixture of exponentials). The paper presents a algorithm for calculating the parameters of the hyperexponential distribution components, which is based on a recursive selection of parameters. This algorithm allows you to analyze various models of queues, including G/G/1. It is shown that the approach under consideration is applicable to the approxi-mation of monotonically decreasing distributions, including those with a "heavy tail". Examples of approximation of Pareto and Weibull distributions are given.

Inferring the ecology of north-Pacific albacore tuna from catch-and-effort data

Catch-and-effort data are among the primary sources of information for assessing the status of terrestrial wildlife and fish. In fishery science, elaborate stock-assessment models are fitted to such data in order to estimate fish-population sizes and guide management decisions. Given the importance of catch-and-effort data, we scoured a comprehensive dataset pertaining to albacore tuna (Thunnus alalunga) in the north Pacific Ocean for novel ecological information content about this commercially valuable species. Specifically, we used unsupervised learning based on finite mixture modelling to reveal that the north Pacific albacore-tuna stock can be divided into four pseudo-cohorts. We discovered that smaller body mass pseudo-cohorts inhabit relatively high—subtropical to temperate—latitudes, with hotspots off the coast of Japan. Larger body mass pseudo-cohorts inhabit lower—tropical to subtropical—latitudes, with hotspots in the western and central north Pacific. These results offer evidence that albacore tuna prefer different habitats depending on their body mass, and point to long-term migratory routes for the species that the current tagging technology is unlikely to capture in full. We discuss the implications of the results for data-driven modelling of albacore tuna in the north Pacific, as well as the management of the north Pacific albacore-tuna fishery.

Uncovering circadian rhythms in metabolic longitudinal data: A Bayesian latent class modeling approach.

Researchers in biology and medicine have increasingly focused on characterizing circadian rhythms and their potential impact on disease. Understanding circadian variation in metabolomics, the study of chemical processes involving metabolites may provide insight into important aspects of biological mechanism. Of scientific importance is developing a statistical rigorous approach for characterizing different types of 24-hour patterns among high dimensional longitudinal metabolites. We develop a latent class approach to incorporate variation in 24-hour patterns across metabolites where profiles are modeled with finite mixtures of distinct shape-invariant circadian curves that themselves incorporate variation in amplitude and phase across metabolites. An efficient Markov chain Monte Carlo sampling is used to carry out Bayesian posterior computation. When the model was fit separately by individual to the data from a small group of participants, two distinct 24-hour rhythms were identified, with one being sinusoidal and the other being more complex with multiple peaks. Interestingly, the latent pattern associated with circadian variation (simple sinusoidal curve) had a similar phase across the three participants, while the more complex latent pattern reflecting diurnal variation differed across individual. The results suggested that this modeling framework can be used to separate 24-hour rhythms into an endogenous circadian and one or more exogenous diurnal patterns in describing human metabolism.

STATISTICAL METHOD FOR EMPIRICAL TESTING OF COMPETING THEORY IN ANAMBRA STATE POLYTECHNIC, MGBAKWU..

Empirical testing of competing theories lies at the heart of social science and applied Science research. We demonstrate that a well-known class of statistical models, called finite mixture models, provides an effective way of rival theory testing. In the proposed framework, each observation is assumed to be generated either from statistical models implied by one of the competing theories or more generally from a weighted combination of multiple statistical models under consideration. Researchers can then estimate the probability that a specific observation is consistent with each rival theory. By modeling this probability with covariates, one can also explore the condition under which a particular theory applies. We discuss a principles way to identify a list of observations that are statistically consistent with each theory and propose measure of the overall performance of each competing theory. We illustrate the relatives’ advantages of our method over existing methods through empirical and stimulation studies.

EVALUATING CREDIT RISK MODELS

Empirical testing of competing theories lies at the heart of social science and applied Science research. We demonstrate that a well-known class of statistical models, called finite mixture models, provides an effective way of rival theory testing. In the proposed framework, each observation is assumed to be generated either from statistical models implied by one of the competing theories or more generally from a weighted combination of multiple statistical models under consideration. Researchers can then estimate the probability that a specific observation is consistent with each rival theory. By modeling this probability with covariates, one can also explore the condition under which a particular theory applies. We discuss a principles way to identify a list of observations that are statistically consistent with each theory and propose measure of the overall performance of each competing theory. We illustrate the relatives’ advantages of our method over existing methods through empirical and stimulation studies.

CSSQ: a ChIP-seq signal quantifier pipeline.

Chromatin immunoprecipitation followed by sequencing (ChIP-seq) has revolutionized the studies of epigenomes and the massive increase in ChIP-seq datasets calls for robust and user-friendly computational tools for quantitative ChIP-seq. Quantitative ChIP-seq comparisons have been challenging due to noisiness and variations inherent to ChIP-seq and epigenomes. By employing innovative statistical approaches specially catered to ChIP-seq data distribution and sophisticated simulations along with extensive benchmarking studies, we developed and validated CSSQ as a nimble statistical analysis pipeline capable of differential binding analysis across ChIP-seq datasets with high confidence and sensitivity and low false discovery rate with any defined regions. CSSQ models ChIP-seq data as a finite mixture of Gaussians faithfully that reflects ChIP-seq data distribution. By a combination of Anscombe transformation, k-means clustering, estimated maximum normalization, CSSQ minimizes noise and bias from experimental variations. Further, CSSQ utilizes a non-parametric approach and incorporates comparisons under the null hypothesis by unaudited column permutation to perform robust statistical tests to account for fewer replicates of ChIP-seq datasets. In sum, we present CSSQ as a powerful statistical computational pipeline tailored for ChIP-seq data quantitation and a timely addition to the tool kits of differential binding analysis to decipher epigenomes.

Finite mixtures of mean-parameterized Conway-Maxwell-Poisson models.

The online version contains supplementary material available at 10.1007/s00362-023-01452-x.