Handling the effect of non-response in graphical models for longitudinal data

In this paper we investigated the use of attrition weights to cope with non-response when selecting graphical chain models for longitudinal data. We proposed a parametric bootstrap approach to account for the extra variability introduced by the estimation of the weights and compared this with results using standard test procedures.     

Bayesian Poisson models for the graphical combination of dependent expert information

A supra-Bayesian (SB) wants to combine the information from a group of k experts to produce her distribution of a probability θ. Each expert gives his counts of what he thinks are the numbers of successes and failures in a sequence of independent trials, each with probability θ of success. These counts, used as a surrogate for each expert's own individual probability assessment (together with his associated level of confidence in his estimate), allow the SB to build various plausible conjugate models. Such models reflect her beliefs about the reliability of different experts and take account of different possible patterns of overlap of information between them. Corresponding combination rules are then obtained and compared with other more established rules and their properties examined.     

Exact estimation of multiple directed acyclic graphs

This paper considers structure learning for multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs. Unlike previous work, we do not require that the vertices in each DAG share a common ordering. Furthermore, we allow for (potentially unknown) dependency structure between the DAGs. Results are presented on both simulated data and fMRI data obtained from multiple subjects.     

An efficient nonparametric test for bivariate two-sample location problem

We propose a new test for the two-sample bivariate location problem. The proposed test statistic has a U-statistic representation with a degenerate kernel. The limiting distribution is found for the proposed test statistic. The power of the test is compared using Monte Carlo simulation to the tests of Blumen [I. Blumen, A new bivariate sign-test for location, Journal of the American Statistical Association 53 (1958) 448–456], Mardia [K.V. Mardia, A non-parametric test for the bivariate two-sample location problem, Journal of the Royal Statistical Society, Series B 29 (1967) 320–342], Peters and Randles [D. Peters, R.H. Randles, A bivariate signed-rank test for the two-sample location problem, Journal of the Royal Statistical Society, Series B 53 (1991) 493–504], LaRocque, Tardif and van Eeden [D. LaRocque, S. Tardif, C. van Eeden, An affine-invariant generalization of the Wilcoxon signed-rank test for the bivariate location problem, Australian and New Zealand Journal of Statistics 45 (2003) 153–165], and Baringhaus and Franz [L. Baringhaus, C. Franz, On a new multivariate two-sample test, Journal of Multivariate Analysis 88 (2004) 190–206]. Under the bivariate normal and bivariate t distributions the proposed test was more powerful than the competitors for almost every change in location. Under the other distributions the proposed test reached the desired power of one at a faster rate than the other tests in the simulation study. Application of the test is presented using bivariate data from a synthetic and a real-life data set.     

A RESTRICTED MAXIMUM LIKELIHOOD PROCEDURE FOR ESTIMATING THE VARIANCE FUNCTION OF AN IMMUNOASSAY

Restricted maximum likelihood (REML) is a procedure for estimating a variance function in a heteroscedastic linear model. Although REML has been extended to non-linear models, the case in which the data are dominated by replicated observations with unknown values of the independent variable of interest, such as the concentration of a substance in a blood sample, has not been considered. We derive a REML procedure for an immunoassay and show that the resulting estimator is superior to those currently being used. Some interesting properties of the REML estimator are derived, and its relationship to other estimators is discussed.     

Maximum likelihood analysis of the mixed model: the balanced case

The primary purpose of this paper is to develop, analytically, the inverse of the covariance matrix for the mixed analysis-of-variance model with balanced data. The use of this matrix in the identification of minimal sufficient statistics and in developing the likelihood equations is illustrated.     

Confidence intervals and significance tests for a single trial

Confidence intervals are developed for the location parameter of a continuous, symmetric, unimodal distribution in the casev where only a single observation from the distribution is available. These intervals are similar to those given by Abbott and Rosenblatt (1963), but shorter. The result is extended to include distributions which can be standardized to have unit scale. The procedure is exemplified for the normal distribution and the power of one- and two-sided significance tests are computed under normality.