A Bayesian criterion for selecting super saturated screening designs

The purpose of a screening experiment is to accurately and cost-efficiently identify the few most influential factors from among the many studied. Two types of screening experiments use orthogonal arrays (OAs) and supersaturated designs (SSDs), respectively. The first requires the number of runs n to be a multiple of 4 and greater than the number of factors k, while the second is a bolder approach wherein n<k. In this study, we compare the performance of OAs with SSDs, using both simulation and a method based on the probability of perfect sign recovery under the Lasso. Our findings indicate that for the scenarios considered, OAs that were far from saturation had similar performance to those that were only slightly above saturation, slightly supersaturated designs required effects between 1.5 and 2 times larger than those for the OAs in order to have similar screening performance, and very supersaturated designs were clearly less effective than the OAs even when detecting effects up to three times as large.

Supersaturated designs are an important class of factorial designs in which the number of factors is larger than the number of runs. These designs supply an economical method to perform and analyze industrial experiments. In this paper, we consider generalized Legendre pairs and their corresponding matrices to construct E(s 2)-optimal two-level supersaturated designs suitable for screening experiments. Also, we provide some general theorems which supply several infinite families of E(s 2)-optimal two-level supersaturated designs of various sizes.

A cyclic construction of saturated and supersaturated designs

Supersaturated design for screening factors influencing the preparation of sulfated amides of olive pomace oil fatty acids

CHAPTER 8 - Decision Theoretic and Bayesian Approach in Testing and Estimation

A supersaturated design is a factorial design in which the number of effects to be estimated is greater than the number of runs. It is used in many experiments, for screening purpose, i.e., for studying a large number of factors and identifying the active ones. In this paper, we propose a method for screening out the important factors from a large set of potentially active variables through the symmetrical uncertainty measure combined with the information gain measure. We develop an information theoretical analysis method by using Shannon and some other entropy measures such as Renyi entropy, Havrda–Charvat entropy, and Tsallis entropy, on data and assuming generalized linear models for a Bernoulli response. This method is quite advantageous as it enables us to use supersaturated designs for analyzing data on generalized linear models. Empirical study demonstrates that this method performs well giving low Type I and Type II error rates for any entropy measure we use. Moreover, the proposed method is more efficient when compared to the existing ROC methodology of identifying the significant factors for a dichotomous response in terms of error rates.

This book on experimental design is somewhat similar in flavor to the classic book by G.E

Saturated and supersaturated order-of-addition designs

A special class of supersaturated design, called marginally over saturated design (MOSD), in which the number of variables under investigation (k) is only slightly larger than the number of experimental runs (n), is presented. Several optimality criteria for supersaturated designs are discussed. It is shown that the resolution rank criterion is most appropriate for screening situations. The construction method builds on two major theorems which provide an efficient way to evaluate resolution rank. Examples are given for the cases n=8, 12, 16, and 20. Potential extensions for future work are discussed.

We propose a general Bayesian joint modeling approach to model mixed longitudinal outcomes from the exponential family for taking into account any differential misclassification that may exist among categorical outcomes. Under this framework, outcomes observed without measurement error are related to latent trait variables through generalized linear mixed effect models. The misclassified outcomes are related to the latent class variables, which represent unobserved real states, using mixed hidden Markov models (MHMMs). In addition to enabling the estimation of parameters in prevalence, transition and misclassification probabilities, MHMMs capture cluster level heterogeneity. A transition modeling structure allows the latent trait and latent class variables to depend on observed predictors at the same time period and also on latent trait and latent class variables at previous time periods for each individual. Simulation studies are conducted to make comparisons with traditional models in order to illustrate the gains from the proposed approach. The new approach is applied to data from the Southern California Children Health Study to jointly model questionnaire-based asthma state and multiple lung function measurements in order to gain better insight about the underlying biological mechanism that governs the inter-relationship between asthma state and lung function development.

In this study, three types of Bayesian coincident-index models were designed based on modification from the so-called Stock-Watson (S-W) index, i.e. the established economic coincident-index. The S-W index approach is commonly used to estimate parameters using sufficient time series data in composite index. However, the S-W approach in small time series data sets, irregular observations and unbalanced data across time is not well-studied. Essentially, all the problem situations are easily handled under the proposed class of Bayesian models. Therefore, we were motivated to design a new Bayesian S-W coincident-index with application in river water quality index. The river water quality data has been chosen due to the availability of small, unbalanced data sets and irregular observations at particular time in selected sampling sites. We tested all the new algorithms which are based on the three coincident-index model i.e. model with no lag, model with first order lag in the water quality variables and model with a lag for unobserved water quality index. We used Bayesian model comparison criterion to choose the best coincident-index model. Deviance Information Criteria (DIC) was performed as a criterion for selecting models since its application to a variety of data-diagnostic models was not well-discussed. Sensitivity model analyses for all models were also reported. The results showed that the model with σ prior 2 was the most appropriate for the Langat river water quality data in the selected sampling sites. The results also showed that that the third model with σ prior 2 for all sampling sites was the most adequate.

Journal Article Market Structure and Innovation Get access Market Structure and Innovation. By Morton I. KAMIEN and NANCY L. SCHWARTZ. (Cambridge: Cambridge University Press, 1982. Pp. xi + 241. £17.50 hardback, £6.95 paperback.) P. Lesley Cook P. Lesley Cook University of Sussex Search for other works by this author on: Oxford Academic Google Scholar The Economic Journal, Volume 92, Issue 368, 1 December 1982, Pages 985–987, https://doi.org/10.2307/2232689 Published: 01 December 1982

Let X 1,…, X n be i.i.d. random variables from an unknown cumulative distribution function F defined on the real line ℝ. No assumptions are made on the unknown F. The problem is to predict the empirical distribution function of a future sample Y = (Y 1,…,Y m ) from the distribution function F on the basis of the observations X 1,…, X n . To solve the problem, a decision theoretic approach is used. In certain situations, when for example a weighted quadratic loss function is used in the prediction problem, the problem of finding the minimax predictor of the empirical distribution function can be reduced to the problem of minimax estimation of the cumulative distribution function F under a composite weighted quadratic loss function. In such a case, a general method of finding minimax predictors of is presented. The method is also useful when no equalizer rule is available. The problem of prediction considered refers also to prediction of the empirical lifetime distribution function and may have some practical significance. For example, the results enable to predict, under the minimax criterion, the number of devices (from among all the m ones) which will fail up to any fixed time t 0.

Estimation of the eigenvalues of noncentrality parameter matrix in noncentral Wishart distribution

In this paper, the design of reliability sampling plans for the Pareto lifetime model under progressive Type-II right censoring is considered. Sampling plans are derived using the decision theoretic approach with a suitable loss or cost function that consists of sampling cost, rejection cost, and acceptance cost. The decision rule is based on the estimated reliability function. Plans are constructed within the Bayesian context using the natural conjugate prior. Simulations for evaluating the Bayes risk are carried out and the optimal sampling plans are reported for various sample sizes, observed number of failures and removal probabilities.