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An exchange algorithm for optimal calibration of items in computerized achievement tests

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2021年 157卷 107177-107177页

作者： Ul Hassan, Mahmood Miller, Frank Stockholm Univ Dept Stat S-10691 Stockholm Sweden

The importance of large scale achievement tests, like national tests in school, eligibility tests for university, or international assessments for evaluation of students, is increasing. Pretesting of questions for the above mentioned tests is done to determine characteristic properties of the questions by adding them to an ordinary achievement test. If computerized tests are used, it has been shown using optimal experimental design methods that it is efficient to assign pretest questions to examinees based on their abilities. The specific distribution of abilities of the available examinees are considered and restricted optimal designs are applied. A new algorithm is developed which builds on an equivalence theorem. It discretizes the design space with the possibility to change the grid adaptively during the run, makes use of an exchange idea and filters computed designs. It is illustrated how the algorithm works through some examples as well as how convergence can be checked. The new algorithm is flexible and can be used even if different models are assumed for different questions. (C) 2021 The Author(s). Published by Elsevier B.V.

关键词： Achievement tests Computerized tests exchange algorithm Experimental design Item response model Optimal restricted design

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A clustering-based coordinate exchange algorithm for generating G-optimal experimental designs

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2016年第8期86卷 1582-1604页

作者： Saleh, Moein Pan, Rong Arizona State Univ Sch Comp Informat & Decis Syst Engn Tempe AZ USA

In the optimal experimental design literature, the G-optimality is defined as minimizing the maximum prediction variance over the entire experimental design space. Although the G-optimality is a highly desirable property in many applications, there are few computer algorithms developed for constructing G-optimal designs. Some existing methods employ an exhaustive search over all candidate designs, which is time-consuming and inefficient. In this paper, a new algorithm for constructing G-optimal experimental designs is developed for both linear and generalized linear models. The new algorithm is made based on the clustering of candidate or evaluation points over the design space and it is a combination of point exchange algorithm and coordinate exchange algorithm. In addition, a robust design algorithm is proposed for generalized linear models with modification of an existing method. The proposed algorithm are compared with the methods proposed by Rodriguez et al. [Generating and assessing exact G-optimal designs. J. Qual. Technol. 2010;42(1):3-20] and Borkowski [Using a genetic algorithm to generate small exact response surface designs. J. Prob. Stat. Sci. 2003;1(1):65-88] for linear models and with the simulated annealing method and the genetic algorithm for generalized linear models through several examples in terms of the G-efficiency and computation time. The result shows that the proposed algorithm can obtain a design with higher G-efficiency in a much shorter time. Moreover, the computation time of the proposed algorithm only increases polynomially when the size of model increases.

关键词： K-means clustering alphabetical optimal design robust design generalized linear models exchange algorithm

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An Adaptive exchange algorithm for Sampling From Distributions With Intractable Normalizing Constants

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2016年第513期111卷 377-393页

作者： Liang, Faming Jin, Ick Hoon Song, Qifan Liu, Jun S. Univ Florida Dept Biostat Gainesville FL 32611 USA Univ Notre Dame Dept Appl & Computat Math & Stat Notre Dame IN 46556 USA Ohio State Univ Ctr Biostat Columbus OH 43210 USA Purdue Univ Dept Stat W Lafayette IN 47906 USA Harvard Univ Dept Stat Sci Ctr 7151 Oxford St Cambridge MA 02138 USA

Sampling from the posterior distribution for a model whose normalizing constant is intractable is a long-standing problem in statistical research. We propose a new algorithm, adaptive auxiliary variable exchange algorithm, or, in short, adaptive exchange (AEX) algorithm, to tackle this problem. The new algorithm can be viewed as a MCMC extension of the exchange algorithm, which generates auxiliary variables via an importance sampling procedure from a Markov chain running in parallel. The convergence of the algorithm is established under mild conditions. Compared to the exchange algorithm, the new algorithm removes the requirement that the auxiliary variables must be drawn using a perfect sampler, and thus can be applied to many models for which the perfect sampler is not available or very expensive. Compared to the approximate exchange algorithms, such as the double Metropolis-Hastings sampler, the new algorithm overcomes their theoretical difficulty in convergence. The new algorithm is tested on the spatial autologistic and autonormal models. The numerical results indicate that the new algorithm is particularly useful for the problems for which the underlying system is strongly dependent. Supplementary materials for this article are available online.

关键词： Autologistic model exchange algorithm Intractable normalizing constant Stochastic approximation Monte Carlo

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Particle swarm exchange algorithms with applications in generating optimal model-discrimination designs

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QUALITY ENGINEERING 2022年第3期34卷 305-321页

作者： Chen, Ping-Yang Chen, Ray-Bing Li, Jui-Pin Li, William Natl Cheng Kung Univ Dept Stat Tainan Taiwan Natl Cheng Kung Univ Inst Data Sci Tainan Taiwan Shanghai Jiao Tong Univ Shanghai Adv Inst Finance Shanghai Peoples R China

exchange-type algorithms have been commonly used to construct optimal designs. As these algorithms may converge to a local optimum, the typical procedure requires the use of several randomly chosen initial designs. Thus, the search for the optimal design can be conducted by performing several independent optimizations. We propose a general framework that combines exchange algorithms with particle swarm intelligence techniques. The main strategy is to represent each initial design as a particle and make the algorithm share information from various converging paths from those initial designs. This amounts to conducting one coordinated optimization instead of several independent optimizations. The proposed general algorithm is called the particle swarm exchange (PSE) algorithm. We compare the performance of PSE with those of two commonly used exchange algorithms - the columnwise-pairwise (CP) exchange algorithm of Li and Wu (1997) for designs with structural requirements and the coordinate exchange algorithm of Meyer and Nachtsheim (1995) for designs without such requirements. In the context of model-robust discriminating designs, we demonstrate that PSE typically performs as well as or, very often, better than the corresponding pure exchange algorithms.

关键词： Columnwise-pairwise exchange algorithm coordinate exchange algorithm exchange algorithm model-discrimination design swarm intelligence

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Exponentiality of the exchange algorithm for finding another room-partitioning

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DISCRETE APPLIED MATHEMATICS 2014年第PART 1期164卷 86-91页

作者： Edmonds, Jack Sanita, Laura Univ Paris 06 Equipe Combinatoire & Optimisat Paris France Ecole Polytech Fed Lausanne Inst Math CH-1015 Lausanne Switzerland

Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning for T is a subset R of the rooms such that each vertex of T is in exactly one room in R. Given a room-partitioning R for T, the exchange algorithm walks from room to room until it finds a second different room-partitioning R'. In fact, this algorithm generalizes the Lemke-Howson algorithm for finding a Nash equilibrium for two-person games. In this paper, we show that the running time of the exchange algorithm is not polynomial relative to the number of rooms, by constructing a sequence of (planar) instances, in which the algorithm walks from room to room an exponential number of times. We also show a similar result for the problem of finding a second perfect matching in Eulerian graphs. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Room-partitioning exchange algorithm Two-person games

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An algorithm for the simultaneous construction of D-optimal experimental designs

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第9期52卷 4156-4173页

作者： Umelo-Ibemere, Ngozi C. Chigbu, Polycarp E. Fed Univ Technol Owerri Dept Stat Owerri 460114 Nigeria Univ Nigeria Dept Stat Nsukka Nigeria

Construction of optimal multiresponse designs when the responses are measured simultaneously for the same settings of the input variables have been studied. However, in some experiments, the response variables can be measured at different time points and also defined in the same experimental space. The response variables are assumed to be uncorrelated. In this case, simultaneous construction of more than one D-optimal design is required. We present an algorithm for the simultaneous construction of D-optimal designs for these kind of experiments. The algorithm operates on two parallel platforms. On one, the same support points are selected for the response functions. The starting point of the search, direction vector, and step length are computed. On the other, the choice of initial design and exchange of design points are carried out. Examples are given to illustrate the construction of optimal designs using the algorithm. The algorithm converges rapidly and is more economical than constructing D-optimal design for one response function at-a-time.

关键词： D-optimal design exchange algorithm Line search method Multiresponse

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An exact sampler for fully Baysian elastic net

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COMPUTATIONAL STATISTICS 2023年第4期38卷 1721-1734页

作者： Wang, Hai-Bin Wang, Jian Xiamen Univ Sch Math Sci Xiamen 361005 Peoples R China

The elastic net plays an important role in regularization regressions. We develop a new hybrid Gibbs sampler for the fully Bayesian elastic net, in which we make use of the exchange algorithm to draw the penalized parameter from its full conditional posterior with an intractable normalizing constant. A great advantage of the proposed sampler is that it is exact and/or time-saving. Moreover, we consider a novel algorithm to sample the standard deviation of the model error from its full conditional that includes the auxiliary vector no longer. We also incorporate a generalised move step in our approach to improve the convergence further. The performance of the proposed method is demonstrated by four simulated examples and the prostate cancer data, and compared with that of the existing methods.

关键词： Elastic net exchange algorithm Gibbs sampler Linear regression

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Exponentiality of the exchange algorithm for finding another room-partitioning

Exponentiality of the exchange algorithm for finding another...

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1st International Symposium on Combinatorial Optimization (ISCO)

作者： Edmonds, Jack Sanita, Laura Univ Paris 06 Equipe Combinatoire & Optimisat Paris France Ecole Polytech Fed Lausanne Inst Math CH-1015 Lausanne Switzerland

关键词： Room-partitioning exchange algorithm Two-person games

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Multivariate Conway-Maxwell-Poisson Distribution: Sarmanov Method and Doubly Intractable Bayesian Inference

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2023年第2期32卷 483-500页

作者： Piancastelli, Luiza S. C. Friel, Nial Barreto-Souza, Wagner Ombao, Hernando Univ Coll Dublin Sch Math & Stat Dublin Ireland Insight Ctr Data Analyt Dublin Ireland King Abdullah Univ Sci & Technol Stat Program Thuwal Saudi Arabia

In this article, a multivariate count distribution with Conway-Maxwell (COM)-Poisson marginals is proposed. To do this, we develop a modification of the Sarmanov method for constructing multivariate distributions. Our multivariate COM-Poisson (MultCOMP) model has desirable features such as (i) it admits a flexible covariance matrix allowing for both negative and positive nondiagonal entries;(ii) it overcomes the limitation of the existing bivariate COM-Poisson distributions in the literature that do not have COM-Poisson marginals;(iii) it allows for the analysis of multivariate counts and is not just limited to bivariate counts. Inferential challenges are presented by the likelihood specification as it depends on a number of intractable normalizing constants involving the model parameters. These obstacles motivate us to propose Bayesian inferential approaches where the resulting doubly intractable posterior is handled with via the noisy exchange algorithm or the Grouped Independence Metropolis-Hastings algorithm. Numerical experiments based on simulations are presented to illustrate the proposed Bayesian approach. We demonstrate the potential of the MultCOMP model through a real data application on the numbers of goals scored by the home and away teams in the English Premier League from 2018 to 2021. Here, our interest is to assess the effect of a lack of crowds during the COVID-19 pandemic on the well-known home team advantage. A MultCOMP model fit shows that there is evidence of a decreased number of goals scored by the home team, not accompanied by a reduced score from the opponent. Hence, our analysis suggests a smaller home team advantage in the absence of crowds, which agrees with the opinion of several football experts. Supplementary materials for this article are available online.

关键词： Bayesian inference Conway-Maxwell-Poisson distribution exchange algorithm Multivariate count data Pseudo-marginal Monte Carlo Thermodynamic integration

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Generating optimal order-of-addition designs with flexible run sizes

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2022年第0期218卷 147-163页

作者： Tsai, Shin-Fu Natl Taiwan Univ Dept Agron Taipei 10617 Taiwan

A series of optimal designs with flexible run sizes is proposed in this paper for designing order-of-addition experiments. Because the full design can be partitioned into several isotopic Latin squares, a fractional design can be obtained by juxtaposing some selected Latin squares according to a particular optimality criterion. A computer-assisted search procedure is first implemented to generate optimal designs with small to moderate run sizes. Based on the computer-generated designs, a recursive method is then used to construct optimal designs with large run sizes. In addition, two practical techniques are introduced to obtain new optimal or near-optimal designs via existing optimal designs. The proposed designs are compared with competing designs generated by conventional software. The results show that the proposed designs are often more efficient for estimating the unknown parameters. A catalogue of optimal designs and near-optimal designs is provided as a reference for future work. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Computer-generated design exchange algorithm Latin square Optimal design Pairwise order model

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