Journal of Data Science

This paper proposes a nonuniform subsampling method for finite mixtures of regression models to reduce large data computational tasks. A general estimator based on a subsample is investigated, and its asymptotic normality is established. We assign optimal subsampling probabilities to data points that minimize the asymptotic mean squared errors of the general estimator and linearly transformed estimators. Since the proposed probabilities depend on unknown parameters, an implementable algorithm is developed. We first approximate the optimal subsampling probabilities using a pilot sample. After that, we select a subsample using the approximated subsampling probabilities and compute estimates using the subsample. We evaluate the proposed method in a simulation study and present a real data example using appliance energy data.

Abstract: Identification of representative regimes of wave height and direction under different wind conditions is complicated by issues that relate to the specification of the joint distribution of variables that are defined on linear and circular supports and the occurrence of missing values. We take a latent-class approach and jointly model wave and wind data by a finite mixture of conditionally independent Gamma and von Mises distributions. Maximum-likelihood estimates of parameters are obtained by exploiting a suitable EM algorithm that allows for missing data. The proposed model is validated on hourly marine data obtained from a buoy and two tide gauges in the Adriatic Sea.

Abstract: The null distribution of the likelihood ratio test (LRT) of a onecomponent normal model versus two-component normal mixture model is

Abstract: In maximum likelihood exploratory factor analysis, the estimates of unique variances can often turn out to be zero or negative, which makes no sense from a statistical point of view. In order to overcome this difficulty, we employ a Bayesian approach by specifying a prior distribution for the variances of unique factors. The factor analysis model is estimated by EM algorithm, for which we provide the expectation and maximization steps within a general framework of EM algorithms. Crucial issues in Bayesian factor analysis model are the choice of adjusted parameters including the number of factors and also the hyper-parameters for the prior distribution. The choice of these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating a Bayesian factor analysis model. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure. We observe that our modeling procedure prevents the occurrence of improper solutions and also chooses the appropriate number of factors objectively.

Abstract: Mixture of Weibull distributions has wide application in modeling of heterogeneous data sets. The parameter estimation is one of the most important problems related to mixture of Weibull distributions. In this pa per, we propose a L-moment estimation method for mixture of two Weibull distributions. The proposed method is compared with maximum likelihood estimation (MLE) method according to the bias, the mean absolute error, the mean total error and completion time of the algorithm (time) by sim ulation study. Also, applications to real data sets are given to show the flexibility and potentiality of the proposed estimation method. The com parison shows that, the proposed method is better than MLE method.

In omics studies, different sources of information about the same set of genes are often available. When the group structure (e.g., gene pathways) within the genes are of interests, we combine the normal hierarchical model with the stochastic block model, through an integrative clustering framework, to model gene expression and gene networks jointly. The integrative framework provides higher accuracy in extensive simulation studies when one or both of the data sources contain noises or when different data sources provide complementary information. An empirical guideline in the choice between integrative versus separate clustering models is proposed. The integrative clustering method is illustrated on the mouse embryo single cell RNAseq and bulk cell microarray data, which identified not only the gene sets shared by both data sources but also the gene sets unique in one data source.

Following the outbreak of COVID-19, various containment measures have been taken, including the use of quarantine. At present, the quarantine period is the same for everyone, since it is implicitly assumed that the incubation period distribution of COVID-19 is the same regardless of age or gender. For testing the effects of age and gender on the incubation period of COVID-19, a novel two-component mixture regression model is proposed. An expectation-maximization (EM) algorithm is adopted to obtain estimates of the parameters of interest, and the simulation results show that the proposed method outperforms the simple regression method and has robustness. The proposed method is applied to a Zhejiang COVID-19 dataset, and it is found that age and gender statistically have no effect on the incubation period of COVID-19, which indicates that the quarantine measure currently in operation is reasonable.