In the third issue of 2017, The Canadian Journal of Statistics presents six papers covering mixture models, Bayesian analysis, adaptive designs, rank tests, and empirical likelihood. 

The issue begins with a review article on Dirichlet process mixture (DPM) models. DPM models have been increasingly employed to specify random partition models that take into account possible patterns within the covariates. BARCELLA,  DE IORIO and BAIO review relevant literature on DPM models that include covariate information in the induced partition of the observations and discuss available variable selection techniques for these models.  

The second article concerns the analysis of data from different sources. When such data are available, it is interesting to develop efficient ways to combine statistical information from the multiple sources. Density ratio models have often been used for this purpose. It seems however that the semiparametric density ratio model, which is useful for such data, has not previously been analyzed using the Bayesian approach. As with the frequentist approach, the Bayesian paradigm provides a way to integrate information from multiple data sources, but in addition, it can fuse this information with subjective or context-based prior information from the analyst. DE OLIVEIRA and KEDEM propose a Bayesian approach for the analysis of a semiparametric density ratio model. The analysis uses a nonparametric likelihood and a transformed Gaussian prior for the “nonparametric part” of the model.

In the third manuscript, SUSKO discusses issues of model selection in the Bayesian framework. With increases in computational power and the advent of simulation-based methods to obtain samples from posteriors, Bayesian methods are increasingly applied to handle complex problems. A fundamental issue is model selection, and Bayes factors provide a natural approach to Bayesian model selection. Using Laplace approximations and illustrative examples, the author demonstrates that Bayes factors can have strong biases toward particular models even in non-nested settings with the same number of parameters. Several easily implemented corrections are shown to provide effective cross-checks for default Bayes Factors.

Response-adaptive designs are important alternatives to equal allocation in clinical trials because equal treatment allocation has been found to have ethical issues. SELVARATNAM, OYET, YI and GADAG discuss the implementation of response-adaptive designs in multi-centre clinical trials. They develop a generalized linear mixed model for analyzing data obtained from such trials and use the maximum likelihood approach to estimate the model parameters. Influence function techniques are applied to derive the asymptotic properties of the proposed estimators. 

The next paper discusses a test procedure pertinent to ranked-set sampling for which the rankings may be either perfect or imperfect. Statistical procedures that assume perfect rankings tend to be more efficient than those that do not when perfect rankings actually hold, but the former may perform poorly if the rankings are imperfect. Several procedures have been developed for testing the null hypothesis of perfect rankings, but these procedures break down if the data are not continuous. FREY and ZHANG develop tests of perfect rankings that can be applied to binary data. To properly control the type I error rate with small samples, they implement a bootstrap version of the test.

The final article investigates the under-coverage issue associated with the empirical likelihood confidence region. In the literature, several methods have been used to address this concern. However, these methods add complexity by requiring extra computation and/or extra theoretical justification. Applying a simple transformation, JING, TSAO and ZHOU construct a transformed version of the empirical likelihood to alleviate the under-coverage problem. The resulting confidence regions are fairly accurate, even in small-sample and multidimensional situations, and their validity is demonstrated using criteria based on accuracy, consistency, and preservation of the geometric appeal of the original empirical likelihood. 

Enjoy the new issue!

Grace Y. Yi

CJS Editor