Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Application of Bayesian regression with singular value decomposition method in association studies for sequence data

Genetic association studies usually involve a large number of single-nucleotide polymorphisms (SNPs) (k) and a relative small sample size (n), which produces the situation that k is much greater than n. Because conventional statistical approaches are unable to deal with multiple SNPs simultaneously when k is much greater than n, single-SNP association studies have been used to identify genes involved in a disease’s pathophysiology, which causes a multiple testing problem. To evaluate the contribution of multiple SNPs simultaneously to disease traits when k is much greater than n, we developed the Bayesian regression with singular value decomposition (BRSVD) method. The method reduces the dimension of the design matrix from k to n by applying singular value decomposition to the design matrix. We evaluated the model using a Markov chain Monte Carlo simulation with Gibbs sampler constructed from the posterior densities driven by conjugate prior densities. Permutation was incorporated to generate empirical p-values. We applied the BRSVD method to the sequence data provided by Genetic Analysis Workshop 17 and found that the BRSVD method is a practical method that can be used to analyze sequence data in comparison to the single-SNP association test and the penalized regression method

Analyzing stochastic computer models: A review with opportunities

This is the author accepted manuscript. The final version is available from the Institute of Mathematical Statistics via the DOI in this record In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models -- providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.European Union FP7DOE LABNational Science Foundatio

Player Pairs Valuation in Ice Hockey

To overcome the shortcomings of simple metrics for evaluating player performance, recent works have introduced more advanced metrics that take into account the context of the players’ actions and perform look-ahead. However, as ice hockey is a team sport, knowing about individual ratings is not enough and coaches want to identify players that play particularly well together. In this paper we therefore extend earlier work for evaluating the performance of players to the related problem of evaluating the performance of player pairs. We experiment with data from seven NHL seasons, discuss the top pairs, and present analyses and insights based on both the absolute and relative ice time together

Exploratory ensemble designs for environmental models using k‐extended Latin Hypercubes

Copyright © 2015 John Wiley & Sons, Ltd.publication-status: AcceptedOpen Access articleIn this paper we present a novel, flexible, and multi-purpose class of designs for initial exploration of the parameter spaces of computer models, such as those used to study many features of the environment. The idea applies existing technology aimed at expanding a Latin Hypercube (LHC) in order to generate initial LHC designs that are composed of many smaller LHCs. The resulting design and its component parts are designed so that each is approximately orthogonal and maximises a measure of coverage of the parameter space. Designs of the type advocated for in this paper are particularly useful when we want to simultaneously quantify parametric uncertainty and any uncertainty due to the initial conditions, boundary conditions, or forcing functions required to run the model. This makes the class of designs particularly suited to environmental models, such as climate models that contain all of these features. The proposed designs are particularly suited to initial exploratory ensembles whose goal is to guide the design of further ensembles aimed at, for example, calibrating the model. We introduce a new emulator diagnostic that exploits the structure of the advocated ensemble designs and allows for the assessment of structural weaknesses in the statistical modelling. We provide illustrations of the method through a simple example and describe a 400 member ensemble of the Nucleus for European Modelling of the Ocean (NEMO) ocean model designed using the method. We build an emulator for NEMO using the created design to illustrate the use of our emulator diagnostic test.Engineering and Physical Sciences Research Council (EPSRC