Local principal curves

Principal components are a well established tool in dimension reduction. The extension to principal curves allows for general smooth curves which pass through the middle of a multidimensional data cloud. In this paper local principal curves are introduced, which are based on the localization of principal component analysis. The proposed algorithm is able to identify closed curves as well as multiple curves which may or may not be connected. For the evaluation of the performance of principal curves as tool for data reduction a measure of coverage is suggested. By use of simulated and real data sets the approach is compared to various alternative concepts of principal curves.     

Approximation of power in multivariate analysis

We consider the calculation of power functions in classical multivariate analysis. In this context, power can be expressed in terms of tail probabilities of certain noncentral distributions. The necessary noncentral distribution theory was developed between the 1940s and 1970s by a number of authors. However, tractable methods for calculating the relevant probabilities have been lacking. In this paper we present simple yet extremely accurate saddlepoint approximations to power functions associated with the following classical test statistics: the likelihood ratio statistic for testing the general linear hypothesis in MANOVA; the likelihood ratio statistic for testing block independence; and Bartlett's modified likelihood ratio statistic for testing equality of covariance matrices.     

A case study in non-centering for data augmentation: Stochastic epidemics

In this paper, we introduce non-centered and partially non-centered MCMC algorithms for stochastic epidemic models. Centered algorithms previously considered in the literature perform adequately well for small data sets. However, due to the high dependence inherent in the models between the missing data and the parameters, the performance of the centered algorithms gets appreciably worse when larger data sets are considered. Therefore non-centered and partially non-centered algorithms are introduced and are shown to out perform the existing centered algorithms.     

Tree-structured subgroup analysis for censored survival data: Validation of computationally inexpensive model selection criteria

The performance of computationally inexpensive model selection criteria in the context of tree-structured subgroup analysis is investigated. It is shown through simulation that no single model selection criterion exhibits a uniformly superior performance over a wide range of scenarios. Therefore, a two-stage approach for model selection is proposed and shown to perform satisfactorily. Applied example of subgroup analysis is presented. Problems associated with tree-structured subgroup analysis are discussed and practical solutions are suggested.     

On Loss Distributions from Installment-Repaid Loans

The banks have been accumulating huge data bases for many years and are increasingly turning to statistics to provide insight into customer behaviour, among other things. Credit risk is an important issue and certain stochastic models have been developed in recent years to describe and predict loan default. Two of the major models currently used in the industry are considered here, and various ways of extending their application to the case where a loan is repaid in installments are explored. The aspect of interest is the probability distribution of the total loss due to repayment default at some time. Thus, the loss distribution is determined by the distribution of times to default, here regarded as a discrete-time survival distribution. In particular, the probabilities of large losses are to be assessed for insurance purposes.     

A Semi-parametric Bayesian Analysis of Survival Data Based on Lévy-driven Processes

In the presence of covariate information, the proportional hazards model is one of the most popular models. In this paper, in a Bayesian nonparametric framework, we use a Markov (Lévy-driven) process to model the baseline hazard rate. Previous Bayesian nonparametric models have been based on neutral to the right processes, which have a number of drawbacks, such as discreteness of the cumulative hazard function. We allow the covariates to be time dependent functions and develop a full posterior analysis via substitution sampling. A detailed illustration is presented.     

Slice sampling for simulation based fitting of spatial data models

An auxiliary variable method based on a slice sampler is shown to provide an attractive simulation-based model fitting strategy for fitting Bayesian models under proper priors. Though broadly applicable, we illustrate in the context of fitting spatial models for geo-referenced or point source data. Spatial modeling within a Bayesian framework offers inferential advantages and the slice sampler provides an algorithm which is essentially off the shelf. Further potential advantages over importance sampling approaches and Metropolis approaches are noted and illustrative examples are supplied.     

Simultaneous Modelling of Survival and Longitudinal Data with an Application to Repeated Quality of Life Measures

In biomedical studies, interest often focuses on the relationship between patients characteristics or some risk factors and both quality of life and survival time of subjects under study. In this paper, we propose a simultaneous modelling of both quality of life and survival time using the observed covariates. Moreover, random effects are introduced into the simultaneous models to account for dependence between quality of life and survival time due to unobserved factors. EM algorithms are used to derive the point estimates for the parameters in the proposed model and profile likelihood function is used to estimate their variances. The asymptotic properties are established for our proposed estimators. Finally, simulation studies are conducted to examine the finite-sample properties of the proposed estimators and a liver transplantation data set is analyzed to illustrate our approaches.     

Two-Stage Estimation in Copula Models Used in Family Studies

In this paper register based family studies provide the motivation for studying a two-stage estimation procedure in copula models for multivariate failure time data. The asymptotic properties of the estimators in both parametric and semi-parametric models are derived, generalising the approach by Shih and Louis (Biometrics vol. 51, pp. 1384–1399, 1995b) and Glidden (Lifetime Data Analysis vol. 6, pp. 141–156, 2000). Because register based family studies often involve very large cohorts a method for analysing a sampled cohort is also derived together with the asymptotic properties of the estimators. The proposed methods are studied in simulations and the estimators are found to be highly efficient. Finally, the methods are applied to a study of mortality in twins.     

Efficient Algorithms for Determining 3-D Bi-Plane Imaging Geometry

Biplane projection imaging is one of the primary methods for imaging and visualizing the cardiovascular system in medicine. A key problem in such a technique is to determine the imaging geometry (i.e., the relative rotation and translation) of two projections so that the 3-D structure can be accurately reconstructed. Based on interesting observations and efficient geometric techniques, we present in this paper new algorithmic solutions for this problem. Comparing with existing optimization-based approaches, our techniques yield better accuracy and have bounded execution time, thus is more suitable for on-line applications. Our techniques can easily detect outliers to further improve the accuracy.This research was supported in part by NIH under USPHS grant numbers HL52567.