Conditions for fourth order rotatability in K dimensions

In this paper, conditions for a set of points to form a rotatable design of order four have been worked out. These condi- tions form the basis for obtaining a set of rotatable designs of order four.     

A simpler way of obtaining non-sIngularity conditions of rotatability

In response surface designs, it is not usually easy to handle the moment matrix X'X, especially for higher orders. This paper presents a method in which the moment matrix of a response surface of any order can be standardized, i.e., X'X splits into a diagonal matrix consisting of sub-matrices of lower order. This eases the calculation of the determinant and the inverse of X'X. The method has been illustrated with applications to second, third and fourth order response surfaces.     

Bayesian mixture models for complex high dimensional count data in phage display experiments

Summary.  Phage display is a biological process that is used to screen random peptide libraries for ligands that bind to a target of interest with high affinity. On the basis of a count data set from an innovative multistage phage display experiment, we propose a class of Bayesian mixture models to cluster peptide counts into three groups that exhibit different display patterns across stages. Among the three groups, the investigators are particularly interested in that with an ascending display pattern in the counts, which implies that the peptides are likely to bind to the target with strong affinity. We apply a Bayesian false discovery rate approach to identify the peptides with the strongest affinity within the group. A list of peptides is obtained, among which important ones with meaningful functions are further validated by biologists. To examine the performance of the Bayesian model, we conduct a simulation study and obtain desirable results.     

A fourth order rotatable design in three dimensions

The necessary and sufficient conditions for a set of points to form a rotatable design of order four have been given by Patel and Arapkoske (1985). One such set of 104 points for three factors which satisfies these conditions is given in this paper.     

Construction of fourth order rotatable designs with estimation of corresponding response surface

This paper provides the reader with a method of selectinga set of points which would form a rotatable design of order four . A fourth order response surface has been fitted and the variance function for the estimated response has been worked out.     

A fourth order rotatable design in four dimensions

Patel and Arap Koske (1985) gave the necessary and sufficient conditions for a set of points to form a rotatable design of order four, A set of 256 points for four factors which satisfies these conditions is given in this paper.