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In this article, we propose an optimal method referred to as SPlit for splitting a dataset into training and testing sets. SPlit is based on the method of support points (SP), which was initially developed for finding the optimal representative points of a continuous distribution. We adapt SP for subsampling from a dataset using a sequential nearest neighbor algorithm. We also extend SP to deal with categorical variables so that SPlit can be applied to both regression and classification problems. The implementation of SPlit on real datasets shows substantial improvement in the worst-case testing performance for several modeling methods compared to the commonly used random splitting procedure. [ABSTRACT FROM AUTHOR]

This paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic (less than six floating-point operations per regression) and shows how two of these algorithms can be combined to form a simple leap and bound technique for finding the best subsets without examining all possible subsets. The result is a reduction of several orders of magnitude in the number of operations required to find the best subsets. [ABSTRACT FROM AUTHOR]

This paper presents the algorithm "DETMAX" whose purpose is to construct experimental designs that are "D-optimal." These are designs for which the determinant of X'X is maximum, where X is the "matrix of independent variables" in the usual linear model y = X Beta + Epsilon. Although the algorithm does not guarantee D-optimality, it has performed well in many cases where D-optimal designs are known. Five examples are given, illustrating the use of DETMAX to construct designs "from scratch" and to augment existing data. A FORTRAN listing is available on request. [ABSTRACT FROM AUTHOR]

For studying k variables in N runs, all 2[sup k-p] designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs. [ABSTRACT FROM AUTHOR]

In this paper the percentage points for the ESD, KUR, and RST many-outlier procedures that were introduced in Rosner (1975) are presented. A brief description of these procedures and some of the issues involved with evaluating their power are presented in Section 1. The algorithm used to estimate their percentage points is given in Section 2, and percentage points for N = 20(10)60(20)100 for k = 2(1)5 are presented. An example to illustrate the use of these percentage points is given in Section 3. Related investigations conducted by the author are reported in Section 4. [ABSTRACT FROM AUTHOR]

The W transformation greatly reduces the computational burden in obtaining maximum likelihood estimates for the mixed A.O.V. model. However, effective optimization methods for maximizing the likelihood must compute the matrix W at each iteration. This paper develops an efficient Cholesky type algorithm for forming W. [ABSTRACT FROM AUTHOR]

This paper proposes a production model for the currant control of the number of defectives by an np-chart. An algorithm for determining the most economic control parameters is presented. An exceedingly simple procedure is suggested for designing control plans which approximate in cost the most economic control plans. This procedure is applicable at the workshop level. [ABSTRACT FROM AUTHOR]

This paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic (less than s x floating-point operations per regression) and shows how two of these algorithms can be combined to form simple leap and bound technique for finding the best subsets without examining all possible subsets. The result is a reduction of several orders of magnitude in the number of operations required to find the best subsets. [ABSTRACT FROM AUTHOR]

The W transformation is needed at each step in the maximum likelihood or restricted maximum likelihood procedure for estimation of the parameters of the mixed A.O.V. model. This paper develops an efficient algorithm for computing the W transformation needing only about a dozen lines of Fortran or PL/l code. [ABSTRACT FROM AUTHOR]

Data extracted from social media platforms are both large in scale and complex in nature, since they contain both unstructured text, as well as structured data, such as time stamps and interactions between users. A key question for such platforms is to determine influential users, in the sense that they generate interactions between members of the platform. Common measures used both in the academic literature and by companies that provide analytics services are variants of the popular web-search PageRank algorithm applied to networks that capture connections between users. In this work, we develop a modeling framework using multivariate interacting counting processes to capture the detailed actions that users undertake on such platforms, namely posting original content, reposting and/or mentioning other users’ postings. Based on the proposed model, we also derive a novel influence measure. We discuss estimation of the model parameters through maximum likelihood and establish their asymptotic properties. The proposed model and the accompanying influence measure are illustrated on a dataset covering a five-year period of the Twitter actions of the members of the U.S. Senate, as well as mainstream news organizations and media personalities. Supplementary material is available online including computer code, data, and derivation details. [ABSTRACT FROM PUBLISHER]

This article considers deterministic computer experiments with real-valued tuning parameters which determine the accuracy of the numerical algorithm. A prominent example is finite-element analysis with its mesh density as the tuning parameter. The aim of this work is to integrate computer outputs with different tuning parameters. Novel nonstationary Gaussian process models are proposed to establish a framework consistent with the results in numerical analysis. Numerical studies show the advantages of the proposed method over existing methods. The methodology is illustrated with a problem in casting simulation. Supplementary material for this article is available online. [ABSTRACT FROM PUBLISHER]

This article proposes a Bayesian method for model selection in fractionated split plot experiments. We employ a Bayesian hierarchical model that takes into account the split plot error structure. Expressions for computing the posterior model probability and other important posterior quantities that require evaluation of at most two unidimensional integrals are derived. A novel algorithm called combined global and local search is proposed to find models with high posterior probabilities and to estimate posterior model probabilities. The proposed method is illustrated with the analysis of two real robust design experiments. Simulation studies demonstrate that the method has good performance. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Many researchers use computer simulators as experimental tools, especially when physical experiments are infeasible. When computer codes are computationally intensive, nonparametric predictors can be fitted to training data for detailed exploration of the input–output relationship. The accuracy of such flexible predictors is enhanced by taking training inputs to be “space-filling.” If there are inputs that have little or no effect on the response, it is desirable that the design be “noncollapsing” in the sense of having space-filling lower dimensional projections. This article describes an algorithm for constructing noncollapsing space-filling designs for bounded input regions that are of possibly high dimension. Online supplementary materials provide the code for the algorithm, examples of its use, and show its performance in multiple settings. [ABSTRACT FROM AUTHOR]

The analysis of data streams requires methods which can cope with a very high volume of data points. Under the requirement that algorithms must have constant computational complexity and a fixed amount of memory, we develop a framework for detecting changes in data streams when the distributional form of the stream variables is unknown. We consider the general problem of detecting a change in the location and/or scale parameter of a stream of random variables, and adapt several nonparametric hypothesis tests to create a streaming change detection algorithm. This algorithm uses a test statistic with a null distribution independent of the data. This allows a desired rate of false alarms to be maintained for any stream even when its distribution is unknown. Our method is based on hypothesis tests which involve ranking data points, and we propose a method for calculating these ranks online in a manner which respects the constraints of data stream analysis. [ABSTRACT FROM AUTHOR]

Control charts based on generalized likelihood ratio (GLR) tests are attractive from both theoretical and practical points of view. In particular, in the case of an autocorrelated process, the GLR test uses the information contained in the time-varying response after a change and, as shown by Apley and Shi, is able to outperfom traditional control charts applied to residuals. In addition, a GLR chart provides estimates of the magnitude and the time of occurrence of the change. In this article we present a practical approach to implementating GLR charts for monitoring an autoregressive moving average process assuming that only a phase I sample is available. The proposed approach, based on automatic time series identification, estimates the GLR control limits through stochastic approximation using bootstrap resampling and thus is able to take into account the uncertainty about the underlying model. A Monte Carlo study shows that our methodology can be used to design, in a semiautomatic fashion, a GLR chart with a prescribed rate of false alarms when as few as 50 phase I observations are available. A real example is used to illustrate the designing procedure. [ABSTRACT FROM AUTHOR]

In this article we propose a robust probabilistic multivariate calibration (RPMC) model in an attempt to identify linear relationships between two sets of observed variables contaminated with outliers. Instead of the Gaussian assumptions that predominate in classical statistical models, RPMC is closely related with the multivariate Student t-distribution over noises and latent variables. Thus RPMC diminishes the effect of outlying data points by regulating the thickness of the distribution tails. RPMC is essentially a robustified version of the supervised probabilistic principal component analysis (SPPCA) that has emerged recently. We show that RPMC encompasses probabilistic principal component analysis and SPPCA as limiting cases. We also derive an efficient EM algorithm for parameter estimation in RPMC. Based on a probabilistic description of latent variables, we present a procedure for the detection of outliers. The experimental results from both simulated examples and real life data sets demonstrate the effectiveness and robustness of our proposed approach. [ABSTRACT FROM AUTHOR]

We propose an algorithm that incorporates both combinatorial and heuristic optimization methods for generating D-efficient factorial designs. This includes an approach that can automatically construct more than 115,000 orthogonal arrays, including at least one array for every known specification with fewer than 144 runs. The algorithm tries various initialization and iteration methods, chooses the most promising method, and then applies more computational effort with the chosen method. The algorithm can make orthogonal and nearly-orthogonal arrays, and it can accommodate restrictions, interactions, and large designs. Usage requires minimal expertise and input. Applications in the area of optimal product design, choice modeling, and marketing research are discussed. [ABSTRACT FROM AUTHOR]

Presents a study which developed a multistage algorithm that clusters datasets and filters out observations classified by these clusters. Categories of clustering algorithms; Overview of two case studies in the applied sciences that would benefit from the methodology for clustering data; Methodology used in the study; Application of the clustering method to software and tomography datasets.

Examines a procedure for multivariate outlier detection. Application of affine equivariant algorithm in outlier detection; Detection of the presence of outliers based on the behavior of the kurtosis coefficient; Motivation for using orthogonal directions in outlier detection.

Features a study which presented a multivariate outlier-detection procedure and a robust estimator for the covariance matrix. Use of information obtained from projections onto the directions that maximize and minimize the kurtosis coefficient of the projected data; Impact of the presence of outlier on the kurtosis values; Description of the algorithm used in the study; Computation of the projection directions.

The authors reflect on the additional improvements in Dolt algorithm and its use in Bayesian statistics. They note that the method can be improved through better choice of matrix using the first approximation computation. They suggest that some evaluation sites must be added concerning the placement of nonnegligible mass outside the points by the posterior density based on the nanowire experiment. They add that the approach is considered a useful tool for Bayesian analysis.

The authors discuss the methods for clustering spatially indexed time-dependent curves. The authors say that they clarify the interaction of the model with data which was indicated in the article by Jiang and Serban. They mention the different points which address the data's correlation within spatial units such as the need for classification methods and simple methods for complex data. They add that clustering algorithms such as k-nearest neighbors and k-means dominated the clustering practice.