Computer experiments with both qualitative and quantitative input variables occur frequently in many scientific and engineering applications. How to choose input settings for such experiments is an important issue for accurate statistical analysis, uncertainty quantification and decision making. Sliced Latin hypercube designs are the first systematic approach to address this issue.However, it comes with the increasing cost associated with an increasing large number of level combinations of the qualitative factors. For the reason of run size economy, marginally coupled designs were proposed in which the design for the quantitative factors is a sliced Latin hypercube design with respect to each qualitative factor. The drawback of such designs is that the corresponding data may not be able to capture the effects between any two (and more) qualitative factors and quantitative factors. To balance the run size and design efficiency, we propose a new type of designs, doubly coupled designs, where the design points for the quantitative factors form a sliced Latin hypercube design with respect to the levels of any qualitative factor and with respect to the level combinations of

In medical studies, the minimum p-value method is often used to determine a cutpoint of a continuous biomarker for predictive classification and to assess whether a subset of patients may have different treatment effect than other patients. This method, however, suffers from an issue of type I error inflation when the estimated cutpoint is treated as known. In this paper, we propose bootstrap-based procedures to obtain the valid p-value for the minimum p-value test statistic when the treatment effect is measured by a continuous outcome under both random and fixed designs, regardless of whether the cutpoint is identifiable. In the fixed design case, the test statistic is the supremum of a non-centered random process, whose mean function (i.e. bias) diverges as the sample size goes to infinity even under the null hypothesis. The proposed bootstrap statistic matches asymptotically the diverging bias, and we apply the high-dimensional Gaussian approximation results to establish the asymptotic size validity, as well as the power consistency under local alternatives. The proposed method is applied to a dataset from a clinical trial on advanced colorectal cancer.

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.