Journal of Data Science

Abstract: A Bayesian hierarchical model is developed for multiple com parisons in mixed models with missing values where the population means satisfy a simple order restriction. We employ the Gibbs sampling and Metropolis-within-Gibbs sampling techniques to obtain parameter estimates and estimates of the posterior probabilities of the equality of the mean pairs. The latter estimates are used to test whether any two means are significantly different, and to test the global hypothesis of the equality of all means. The performance of the model is investigated in simulations by means of both multiple imputations and ignoring missingness. We also illustrate the utility of the model in a real data set. The results show that the proposed hierarchical model can effectively unify parameter estimation, multiple imputations, and multiple comparisons in one setting.

Abstract: This paper considers the estimation of lifetime distribution based on missing-censoring data. Using the simple empirical approach rather than the maximum likelihood argument, we obtain the parametric estimations of lifetime distribution under the assumption that the failure time follows exponential or gamma distribution. We also derive the nonparametric estimation for both continuous and discrete failure distributions under the assumption that the censoring distribution is known. The loss of efficiency due to missing-censoring is shown to be generally small if the data model is specified correctly. Identifiability issue of the lifetime distribution with missing-censoring data is also addressed.

Abstract: We consider a fully Bayesian treatment of radial basis function regression, and propose a solution to the instability of basis selection. Indeed, when bases are selected solely according to the magnitude of their posterior inclusion probabilities, it is often the case that many bases in the same neighborhood end up getting selected leading to redundancy and ultimately inaccuracy of the representation. In this paper, we propose a straightforward solution to the problem based on post-processing the sample path yielded by the model space search technique. Specifically, we perform an a posteriori model-based clustering of the sample path via a mixture of Gaussians, and then select the points closer to the means of the Gaussians. Our solution is found to be more stable and yields a better performance on simulated and real tasks.

Abstract: In this paper, we use generalized influence function and generalized Cook distance to measure the local influence of minor perturbation on the modified ridge regression estimator in ridge type linear regression model. The diagnostics under the perturbation of constant variance and individual explanatory variables are obtained when multicollinearity presents among the regressors. Also we proposed a statistic that reveals the influential cases for Mallow’s method which is used to choose modified ridge regression estimator biasing parameter. Two real data sets are used to illustrate our methodologies.

Abstract: The aim of this study is to develop a method for detection of temporomandibular disorder (TMD) based on visual analysis of facial movements. We analyse the motion of colour markers placed on the locations of interest on subjects faces in the video frames. We measured several features from motion patterns of the markers that can be used to distinguish between different classes. In our approach, both static and dynamic features are measured from a number of time sequences for classification of the subjects. A measure of nonlinear dynamics of the variations in the movement of colour markers positioned on the subjects faces was obtained via estimating the maximum Lyapunov exponent. Static features such as the number of outliers and kurtosis have also been evaluated. Then, Support Vector Machines (SVMs) are used to automatically classify all the subjects as belonging to individuals with TMD and healthy subjects.

Abstract: In the absence of definitive trials on the safety and efficacy of drugs, a systematic and careful synthesis of available data may provide critical information to help decision making by policy makers, medical professionals, patients and other stakeholders. However, uncritical and unbalanced use of pooled data to inform decision about important healthcare issues may have consequences that adversely impact public health, stifle innovation, and con found medical science. In this paper, we highlight current methodological issues and discuss advantages and disadvantages of alternative meta-analytic techniques. It is argued that results from pooled data analysis would have maximal reliability and usefulness in decision making if used in a holistic framework that includes presentation of data in light of all available knowledge and effective collaboration among academia, industry, regulatory bodies and other stakeholders.

Abstract: A new set of methods are developed to perform cluster analysis of functions, motivated by a data set consisting of hydraulic gradients at several locations distributed across a wetland complex. The methods build on previous work on clustering of functions, such as Tarpey and Kinateder (2003) and Hitchcock et al. (2007), but explore functions generated from an additive model decomposition (Wood, 2006) of the original time series. Our decomposition targets two aspects of the series, using an adaptive smoother for the trend and circular spline for the diurnal variation in the series. Different measures for comparing locations are discussed, including a method for efficiently clustering time series that are of different lengths using a functional data approach. The complicated nature of these wetlands are highlighted by the shifting group memberships depending on which scale of variation and year of the study are considered.

Abstract: Random Utility models have been shown useful in scaling choice options, as well as in providing a rich source of information about individual differences and perceived similarity relationships among choice alternatives. Modeling of preference data such as rankings was made easier by representing utilities as latent factors in a structural equation modeling framework. In this paper, we extend such an SEM approach to analyze ranking data and other types of ordinal data simultaneously. This combination of both absolute and relative judgment data can enrich our understanding of individual differences in multiple domains including preference and attitude.

Abstract: The power law process (PLP) (i.e., the nonhomogeneous Poisson process with power intensity law) is perhaps the most widely used model for analyzing failure data from reliability growth studies. Statistical inferences and prediction analyses for the PLP with left-truncated data with classical methods were extensively studied by Yu et al. (2008) recently. However, the topics discussed in Yu et al. (2008) only included maximum likelihood estimates and confidence intervals for parameters of interest, hypothesis testing and goodness-of-fit test. In addition, the prediction limits of future failure times for failure-truncated case were also discussed. In this paper, with Bayesian method we consider seven totally different prediciton issues besides point estimates and prediction limits for xn+k. Specifically, we develop estimation and prediction methods for the PLP in the presence of left-truncated data by using the Bayesian method. Bayesian point and credible interval estimates for the parameters of interest are derived. We show how five single-sample and three two-sample issues are addressed by the proposed Bayesian method. Two real examples from an engine development program and a repairable system are used to illustrate the proposed methodologies.

Abstract: For two independent random variables, X and Y, let p = P(X > Y ) + 0.5P(X = Y ), which is sometimes described as a probabilistic measure of effect size. It has been argued that for various reasons, p represents an important and useful way of characterizing how groups differ. In clinical trials, for example, an issue is the likelihood that one method of treatment will be more effective than another. The paper deals with making inferences about p when three or more groups are to be compared. When tied values can occur, the results suggest using a multiple comparison procedure based on an extension of Cliff’s method used in conjunction with Hochberg’s sequentially rejective technique. If tied values occur with probability zero, an alternative method can be argued to have a practical advantage. As for a global test, extant rank-based methods are unsatisfactory given the goal of comparing groups based on p. The one method that performed well in simulations is based in part on the distribution of the difference between each pair of random variables. A bootstrap method is used where a p-value is based on the projection depth of the null vector relative to the bootstrap cloud. The proposed methods are illustrated using data from an intervention study.