We produce reasons and evidence supporting the informal rule that the number of runs for an effective initial computer experiment should be about 10 times the input dimension. Our arguments quantify two key characteristics of computer codes that affect the sample size required for a desired level of accuracy when approximating the code via a Gaussian process (GP). The first characteristic is the total sensitivity of a code output variable to all input variables. The second corresponds to the way this total sensitivity is distributed across the input variables, specifically the possible presence of a few prominent input factors and many impotent ones (effect sparsity). Both measures relate directly to the correlation structure in the GP approximation of the code. In this way, the article moves towards a more formal treatment of sample size for a computer experiment. The evidence supporting these arguments stems primarily from a simulation study and via specific codes modeling climate and ligand activation of G-protein.

Adaptive and sequential experiment design is a well-studied area in numerous domains. We survey and synthesize the work of the online statistical learning paradigm referred to as multi-armed bandits integrating the existing research as a resource for a certain class of online experiments. We first explore the traditional stochastic model of a multi-armed bandit, then explore a taxonomic scheme of complications to that model, for each complication relating it to a specific requirement or consideration of the experiment design context. Finally, at the end of the paper, we present a table of known bounds of regret for all studied algorithms providing both perspectives for future theoretical work and a decision-making tool for practitioners looking for theoretical guarantees. Primary 62K99, 62L05; secondary 68T05. Keywords and phrases: multi-armed bandits, adaptive experiments, sequential experiment design, online experiment design. * Loeppky and Lawrence were partly supported by Natural Sciences and Engineering Research Council of Canada Discovery Grants, grant numbers RGPIN-2015-03895 and RGPIN-341202-12 respectively. 1 imsart-generic ver. 2011/11/15 file: mab-ss-survey.tex date: November 4,

Computer models simulating a physical process are used in many areas of science. Due to the complex nature of these codes it is often necessary to approximate the code, which is typically done using a Gaussian process. In many situations the number of code runs available to build the Guassian process approximation is limited. When the initial design is small or the underlying response surface is complicated this can lead to poor approximations of the code output. In order to improve the fit of the model, sequential design strategies must be employed. In this paper we introduce two simple distance based metrics that can be used to augment an initial design in a batch sequential manner. In addition we propose a sequential updating strategy to an orthogonal array based Latin hypercube sample. We show via various real and simulated examples that the distance metrics and the extension of the orthogonal array based Latin hypercubes work well in practice.

In many industrial applications, the experimenter is interested in estimating some of the main effects and two-factor interactions. In this article we rank two-level orthogonal designs based on the number of estimable models containing a subset of main effects and their associated two-factor interactions. By ranking designs in this way, the experimenter can directly assess the usefulness of the experimental plan for the purpose in mind. We apply the new ranking criterion to the class of all nonisomorphic two-level orthogonal designs with 16 and 20 runs and introduce a computationally efficient algorithm, based on two theoretical results, which will aid in finding designs with larger run sizes. Catalogs of useful designs with 16, 20, 24, and 28 runs are presented.