On Future Directions in Statistical Methodologies – Some Speculations

Abstract. We, as statisticians, are living in interesting times. New scientifically significant questions are waiting for our contributions, new data accumulate at a fast rate, and the rapid increase of computing power gives us unprecedented opportunities to meet these challenges. Yet, many members of our community are still turning the old wheel as if nothing dramatic had happened. There are ideas, methods and techniques which are commonly used but outdated and should be replaced by new ones. Can we expect to see, as has been suggested, a consolidation of statistical methodologies towards a new synthesis, or is perhaps an even wider separation and greater divergence the more likely scenario? In this talk these issues are discussed, and some conjectures and suggestions are made.     

Bayesian Inference from Case–cohort Data with Multiple End-points

Abstract.  In a case–cohort design a random sample from the study cohort, referred as a subcohort, and all the cases outside the subcohort are selected for collecting extra covariate data. The union of the selected subcohort and all cases are referred as the case–cohort set. Such a design is generally employed when the collection of information on an extra covariate for the study cohort is expensive. An advantage of the case–cohort design over more traditional case–control and the nested case–control designs is that it provides a set of controls which can be used for multiple end-points, in which case there is information on some covariates and event follow-up for the whole study cohort. Here, we propose a Bayesian approach to analyse such a case–cohort design as a cohort design with incomplete data on the extra covariate. We construct likelihood expressions when multiple end-points are of interest simultaneously and propose a Bayesian data augmentation method to estimate the model parameters. A simulation study is carried out to illustrate the method and the results are compared with the complete cohort analysis.     

A Method for Bayesian Monotonic Multiple Regression

Abstract. When applicable, an assumed monotonicity property of the regression function w.r.t. covariates has a strong stabilizing effect on the estimates. Because of this, other parametric or structural assumptions may not be needed at all. Although monotonic regression in one dimension is well studied, the question remains whether one can find computationally feasible generalizations to multiple dimensions. Here, we propose a non‐parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure. The monotonic construction is based on marked point processes, where the random point locations and the associated marks (function levels) together form piecewise constant realizations of the regression surfaces. The actual inference is based on model‐averaged results over the realizations. The monotonicity of the construction is enforced by partial ordering constraints, which allows it to asymptotically, with increasing density of support points, approximate the family of all monotonic bounded continuous functions.