This work extends and develops the idea of using functional priors for the design and analysis of three and higher level experiments. Developing a prior distribution for model parameters is challenging because a factor can be qualitative or quantitative. We propose appropriate correlation functions and coding schemes so that the prior distribution is simple and the results interpretable. The prior incorporates well known principles such as effect hierarchy and effect heredity, which helps to resolve the aliasing problems in fractional designs almost automatically. The usefulness of the new approach is illustrated through the analysis of some real experiments.

Orthogonal arrays are used widely in manufacturing and high-technology industries for quality and productivity improvement experiments. For reasons of run size economy or � exibility, nearly-orthogonal arrays are also used. The construction of orthogonal or nearly-orthogonal arrays can be quite challenging. Most existing methods are complex and produce limited types of arrays. This article describes a simple and effective algorithm for constructing mixed-level orthogonal and nearly-orthogonal arrays that can construct a variety of small-run designs with good statistical properties ef � ciently. KEY WORDS: D-optimality; Exchange algorithm; Interchange algorithm; J 2-optimality. 1.

Specification of the linear predictor for a generalised linear model requires determining which variables to include. We consider Bayesian strategies for performing this variable selection. In particular we focus on approaches based on the Gibbs sampler. Such approaches may be implemented using the publically available software BUGS. We illustrate the methods using a simple example. BUGS code is provided in an appendix. 1 Introduction In a Bayesian analysis of a generalised linear model, model uncertainty may be incorporated coherently by specifying prior probabilities for plausible models and calculating posterior probabilities using f(mjy) = f(m)f(yjm) P m2M f(m)f(y jm) ; m 2 M (1.1) where m denotes the model, M is the set of all models under consideration, f (m) is the prior probability of model m and f (yjm; fi m ) the likelihood of the data y under model m. The observed data y contribute to the posterior model probabilities through f(yjm), the marginal likelihood calculated...

Specifying a prior distribution for the large number of parameters in the statistical model is a critical step in a Bayesian approach to the design and analysis of experiments. This article shows that the prior distribution can be induced from a functional prior on the underlying transfer function. The functional prior requires the specification of only a few hyper-parameters and therefore, can be easily implemented in practice. The usefulness of the approach is demonstrated through the analysis of some experiments. The article also proposes a new class of design criteria and establishes their connections with the minimum aberration criterion.

This article concerns adaptive experimentation as a means for making improvements in design of engineering systems. A simple method for experimentation, called “adaptive one-factor-at-a-time,” is described. A mathematical model is proposed and theorems are proven concerning the expected value of the improvement provided and the probability that factor effects will be exploited. It is shown that adaptive one-factor-at-a-time provides a large fraction of the potential improvements if experimental error is not large compared with the main effects and that this degree of improvement is more than that provided by resolution III fractional factorial designs if interactions are not small compared with main effects. The theorems also establish that the method exploits two-factor interactions when they are large and exploits main effects if interactions are small. A case study on design of electric-powered aircraft supports these results.

This tutorial describes some ways that Bayesian methods address problems that arise during simulation studies. This includes quantifying uncertainty about input distributions and parameters, sensitivity analysis, and the selection of the best of several simulated alternatives. Focus is on illustrating the main ideas and their relevance to practical problems. Numerous citations for both introductory and more advanced material provide a launching pad into the Bayesian literature.

The non-geometric Plackett-Burman designs open for an economical screening of many factors in few runs. These designs have traditionally been used as main effect plans assuming interactions to be negligible. If interactions are present, however, a more thorough analysis of the experiments is required to identify the active factors due to the complex alias-patterns of these designs. In this paper we demonstrate the usefulness of two variable selection techniques that account for interactions. One is a best subsets regression procedure guided by the principle of effect heredity. The other is a stepwise regression procedure on subsets of potentially active factors. Both techniques enable a fairly systematic search for the active factors within reasonable computing time. Key words: Effect heredity; Factor sparsity; Regression analysis; Screening; Variable selection. 1 Introduction Screening experiments play an important part of experimental design. Their primary objective is to identify ...

This thesis considers the problem of achieving better system performance through adaptive experiments. For the case of discrete design space, I propose an adaptive One-Factor-at-A-Time (OFAT) experimental design, study its properties and compare its performance to saturated fractional factorial designs. The rationale for adopting the adaptive OFAT design scheme become clear if it is imbedded in a Bayesian framework: it becomes clear that OFAT is an efficient response to step by step accrual of sample information. The Bayesian predictive distribution for the outcome by implementing OFAT and the corresponding principal moments when a natural conjugate prior is assigned to parameters that are not known with certainty are also derived. For the case of compact design space, I expand the treatment of OFAT by the

Abstract: A supersaturated design is a design whose run size is not enough for estimating all the main effects. It is commonly used in screening experiments, where the goals are to identify sparse and dominant active factors with low cost. In this paper, we study a variable selection method via the Dantzig selector, proposed by Candes and Tao (2007), to screen important effects. A graphical procedure and an automated procedure are suggested to accompany with the method. Simulation shows that this method performs well compared to existing methods in the literature and is more efficient at estimating the model size. MSC: primary 62K15; secondary 62J05; 62J07

One of the suggested methods for identifying active factors in screening experiments is the Bayesian approach presented by Box and Meyer (1993). This method has been used successfully in the analysis of a number of both real and simulated data. To our experience however, there are situations where the method appears to be somewhat dependent of the size of both effects and error variance compared with a traditional regression analysis. In addition, when using the 12 run Plackett-Burman design the method often has problem with identifying more than three active factors. In this paper we look closer into the performance of the Box-Meyer method on a few simulated examples using both a 2 5\Gamma1 V fractional factorial design and a 12 run Plackett-Burman design. A simple modification of the Box-Meyer method, where non-significant terms in the individual models are removed, seems to reduce the described problems. Key words: Factor sparsity; Plackett-Burman design; Regression; Variable sel...