THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Big Data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures. The construction of such systems involves many distributed design choices. The end products (e.g., recommendation systems, medical analysis tools, real-time game engines, speech recognizers) thus involve many tunable configuration parameters. These parameters are often specified and hard-coded into the software by various developers or teams. If optimized jointly, these parameters can result in significant improvements. Bayesian optimization is a powerful tool for the joint optimization of design choices that is gaining great popularity in recent years. It promises greater automation so as to increase both product quality and human productivity. This review paper introduces Bayesian optimization, highlights some of its methodological aspects, and showcases a wide range of applications.

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Taking the Human Out of the Loop: A Review of Bayesian Optimization

AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

Many engineering applications are characterized by implicit response functions that are expensive to evaluate and sometimes nonlinear in their behavior, making reliability analysis difficult. This paper develops an efficient reliability analysis method that accurately characterizes the limit state throughout the random variable space. The method begins with a Gaussian process model built from a very small number of samples, and then adaptively chooses where to generate subsequent samples to ensure that the model is accurate in the vicinity of the limit state. The resulting Gaussian process model is then sampled using multimodal adaptive importance sampling to calculate the probability of exceeding (or failing to exceed) the response level of interest. By locating multiple points on or near the limit state, more complex and nonlinear limit states can be modeled, leading to more accurate probability integration. By concentrating the samples in the area where accuracy is important (i.e., in the vicinity of the limit state), only a small number of true function evaluations are required to build a quality surrogate model. The resulting method is both accurate for any arbitrarily shaped limit state and computationally efficient even for expensive response functions. This new method is applied to a collection of example problems including one that analyzes the reliability of a microelectromechanical system device that current available methods have difficulty solving either accurately or efficiently.

Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs...

https://epubs.siam.org/doi/pdf/10.1137/16M1082469

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

Supplementary material to "Modeling an Augmented Lagrangian for Blackbox Constrained Optimization"

Supplementary Material: Modeling an Augmented Lagrangian for Blackbox Constrained Optimization

In this paper, we consider two rainfall-runoff computer models. The first model is Matlab-Simulink model which simulates runoff from windrow compost pad (located at the Bioconversion Center in Athens, GA) over a period of time based on rainfall events. The second model is Soil Water Assessment Tool (SWAT) which estimates surface runoff in the Middle Oconee River in Athens, GA. The input parameter spaces of both models are sensitive and high dimensional, the model output for every input combination is a time-series of runoff, and these two computer models generate a wide spectrum of outputs including some that are far from reality. In order to improve the prediction accuracy, in this paper we propose to apply a history matching approach for calibrating these hydrological models, which also gives better insights for improved management of these systems.

Inverse Mapping for Rainfall-Runoff Models using History Matching Approach

In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining features of the relationship between the return and its volatility. Among one of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the current return is a function of the current latent volatility, which is further modeled as an auto-regressive process. In an attempt to make the SVMs more appropriate for complex realistic market behavior, a leverage parameter was introduced in the Taylor SVM, which however led to the violation of the efficient market hypothesis (EMH, a necessary mean-zero condition for the return distribution that prevents arbitrage possibilities). Subsequently, a host of alternative SVMs had been developed and are currently in use. In this paper, we propose mean-corrections for several generalizations of Taylor SVM that capture the complex market behavior as well as satisfy EMH. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, four real-life examples (Oil price, CITI bank stock price, Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs.

A New Class of Discrete-time Stochastic Volatility Model with Correlated Errors

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Comment on article by Vernon et al.

Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs has been extensively investigated. Much of the work has been on a case-by-case basis -- addressing completely randomized designs, randomized block designs, split-plot designs, etc. separately. In this paper we take a more unified approach, developing theoretical results and an efficient relabeling strategy to both construct and check the isomorphism of multi-stage factorial designs with randomization restrictions. The examples presented in this paper particularly focus on split-lot designs.

Pritam Ranjan

Papers

Supplementary Material: Modeling an Augmented Lagrangian for Blackbox Constrained Optimization

Inverse Mapping for Rainfall-Runoff Models using History Matching Approach

A New Class of Discrete-time Stochastic Volatility Model with Correlated Errors

Comment on article by Vernon et al.

Isomorphism Check for $2^n$ Factorial Designs with Randomization Restrictions