Semiparametric Bayesian classification with longitudinal markers

Summary.  We analyse data from a study involving 173 pregnant women. The data are observed values of the β human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random-effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods.     

The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology

For frequency counts, the situation of extra zeros often arises in biomedical applications. This is demonstrated with count data from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Extra zeros, however, violate the variance–mean relationship of the Poisson error structure. This extra-Poisson variation can easily be explained by a special mixture model, the zero-inflated Poisson (ZIP) model. On the basis of the ZIP model, a graphical device is presented which not only summarizes the mixing distribution but also provides visual information about the overall mean. This device can be exploited to evaluate and compare various groups. Ways are discussed to include covariates and to develop an extension of the conventional Poisson regression. Finally, a method to evaluate intervention effects on the basis of the ZIP regression model is described and applied to the data of the Belo Horizonte caries prevention study.     

Hypothesis test for paired samples in the presence of missing data

Missing data are present in almost all statistical analysis. In simple paired design tests, when some subject has one of the involved variables missing in the so-called partially overlapping samples scheme, it is usually discarded for the analysis. The lack of consistency between the information reported in the univariate and multivariate analysis is, perhaps, the main consequence. Although the randomness on the missing mechanism (missingness completely at random) is an usual and needed assumption for this particular situation, missing data presence could lead to serious inconsistencies on the reported conclusions. In this paper, the authors develop a simple and direct procedure which allows using the whole available information in order to perform paired tests. In particular, the proposed methodology is applied to check the equality among the means from two paired samples. In addition, the use of two different resampling techniques is also explored. Finally, real-world data are analysed.     

Multivariate Kendall's tau for change‐point detection in copulas

Statistical procedures for the detection of a change in the dependence structure of a series of multivariate observations are studied in this work. The test statistics that are proposed are $L_1$ , $L_2$ , and $L_{\infty }$ distances computed from vectors of differences of Kendall's tau; two multivariate extensions of Kendall's measure of association are used. Since the distributions of these statistics under the null hypothesis of no change depend on the unknown underlying copula of the vectors, a procedure based on the multiplier central limit theorem is used for the computation of p‐values; the method is shown to be valid both asymptotically and for moderate sample sizes. Alternative versions of the tests that take into account possible breakpoints in the marginal distributions are also investigated. Monte Carlo simulations show that the tests are powerful under many scenarios of change‐point. In addition, two estimators of the time of change are proposed and their efficiency is carefully studied. The methodologies are illustrated on simulated series from the Canadian Regional Climate Model. The Canadian Journal of Statistics 41: 65–82; 2013 © 2012 Statistical Society of Canada     

Random translation of discrete order statistics

We investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose order statistics are related by a random translation. We also provide some examples using the constructive method that we propose.     

Projection Measures And Estimation Variances Of Intensities

The paper investigates random processes of geometrical objects in Euclidean spaces. General properties of the measure of total projections are derived by means of Palm distribution. Explicit formulas for variances of the projection measure are obtained for Poisson point processes of compact sets.

Intensity estimators of fibre (surface) processes are then studied by means of projection measures. Classification of direct and indirect probes is introduced. The indirect sampling design of vertical sections and projections is generalized and its statistical properties derived.     

Nonparametric product partition models for multiple change-points analysis

ABSTRACT

We propose an extension of parametric product partition models. We name our proposal nonparametric product partition models because we associate a random measure instead of a parametric kernel to each set within a random partition. Our methodology does not impose any specific form on the marginal distribution of the observations, allowing us to detect shifts of behaviour even when dealing with heavy-tailed or skewed distributions. We propose a suitable loss function and find the partition of the data having minimum expected loss. We then apply our nonparametric procedure to multiple change-point analysis and compare it with PPMs and with other methodologies that have recently appeared in the literature. Also, in the context of missing data, we exploit the product partition structure in order to estimate the distribution function of each missing value, allowing us to detect change points using the loss function mentioned above. Finally, we present applications to financial as well as genetic data.     

Influence analysis in multivariate linear general models

In this paper we obtain several influence measures for the multivariate linear general model through the approach proposed by Muñoz-Pichardo et al. (1995), which is based on the concept of conditional bias. An interesting charasteristic of this approach is that it does not require any distributional hypothesis. Appling the obtained results to the multivariate regression model, we obtain some measures proposed by other authors. Nevertheless, on the results obtained in this paper, we emphasize two aspects. First, they provide a theoretical foundation for measures proposed by other authors for the mul¬tivariate regression model. Second, they can be applied to any linear model that can be formulated as a particular case of the multivariate linear general model. In particular, we carry out an application to the multivariate analysis of covariance.     

A Bayesian semi-parametric approach to the ordinal calibration problem

ABSTRACT

We introduce a semi-parametric Bayesian approach based on skewed Dirichlet processes priors for location parameters in the ordinal calibration problem. This approach allows the modeling of asymmetrical error distributions. Conditional posterior distributions are implemented, thus allowing the use of Markov chains Monte Carlo to generate the posterior distributions. The methodology is applied to both simulated and real data.