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Combinations of drugs are now ubiquitous in treating complex diseases such as cancer and HIV due to their potential for enhanced efficacy and reduced side effects. The traditional combination experiments of drugs focus primarily on the dose effects of the constituent drugs. However, with the doses of drugs remaining unchanged, different sequences of drug administration may also affect the efficacy endpoint. Such drug effects shall be called as order effects. The common order‐effect linear models are usually inadequate for analyzing combination experiments due to the nonlinear relationships and complex interactions among drugs. In this article, we propose a random field model for order‐effect modeling. This model is flexible, allowing nonlinearities, and interaction effects to be incorporated with a small number of model parameters. Moreover, we propose a subtle experimental design that will collect good quality data for modeling the order effects of drugs with a reasonable run size. A real‐data analysis and simulation studies are given to demonstrate that the proposed design and model are effective in predicting the optimal drug sequences in administration. [ABSTRACT FROM AUTHOR]

For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special cases. In addition to being column-orthogonal, these designs have good space-filling properties in two dimensions. The resulting designs achieve stratifications on s 2 × s or s × s 2 grids, and most column pairs satisfy stratifications on s 2 × s 2 grids. Moreover, many column pairs can achieve stratifications on s 4 × s 2 and s 2 × s 4 grids. Furthermore, the obtained space-filling ODs can have s 6 levels, s 4 levels, and mixed levels, as required for different needs. [ABSTRACT FROM AUTHOR]

A growing trend in engineering and science is to use multiple computer codes with different levels of accuracy to study the same complex system. Strategies are needed to combine the simulation results obtained at different levels of accuracy to produce an efficient surrogate model for prediction. In this paper, we propose an integral model to borrow as much information as possible from the low‐accuracy experiment. We ignore the Markov property assumed before and model the high‐accuracy experiment based on an integral form of the low‐accuracy experiment. The proposed model is more general thus better predictions are expected. Two explicit forms of some matrices and vectors used in our predictions are given. The effectiveness of the proposed model is illustrated with several examples. [ABSTRACT FROM AUTHOR]

Strong orthogonal arrays (SOAs) have received more and more attention recently since they enjoy more desirable space-filling properties than ordinary orthogonal arrays. Among them, the SOAs of strength 2 + are the most advisable as they satisfy the same two-dimensional space-filling property as SOAs of strength 3 while having more columns for given run sizes. In addition, column-orthogonality is also a desirable property for designs of computer experiments. Existing column-orthogonal SOAs of strength 2 + have limited columns. In this paper, we propose a new class of space-filling designs, called group SOAs of strength 2 + , and provide construction methods for such designs. The proposed designs can accommodate more columns than column-orthogonal SOAs of strength 2 + for given run sizes while satisfying similar stratifications and retaining a high proportion of column-orthogonal columns. Orthogonal arrays and difference schemes play important roles in the construction. The construction procedures are easy to implement and a large amount of group SOAs with s 2 levels are constructed where s ≥ 2 is a prime power. In addition, the run sizes of the constructed designs are s times the ones of the orthogonal arrays used in the construction procedure. Thus they are relatively flexible. [ABSTRACT FROM AUTHOR]

Karunanayaka and Tang (2017) introduced a class of compromise designs for estimating main effects under the baseline parameterization. Their approach is to add some runs to the basic one-factor-at-a-time design, and its implementation requires computer search except for the case of adding one run where a theoretical result is available. The reliance on computer search only allowed them to find the limited results from adding up to four runs to the basic one-factor-at-a-time design. In this paper, we provide a systematic construction of compromise designs, without computer search and without restriction on the run size and the number of factors. Closed-form expressions of the bias and efficiency criteria are obtained for the new designs. Both theoretical and empirical studies show that our designs outperform those of Karunanayaka and Tang (2017) saving small-sized problems. • This paper provides a systematic construction of compromise designs under baseline parameterization. • Closed-form expressions of the bias and efficiency criteria are obtained for the new designs. • The new designs outperform those of Karunanayaka and Tang (2017) saving small-sized problems. [ABSTRACT FROM AUTHOR]

A supersaturated design (SSD) is a factorial design whose run size is not enough for estimating all the main effects. Such designs have received much recent interest because of their potential in factor screening experiments. This paper first shows that the design obtained by the Kronecker sum of a balanced design and a generalized Hadamard matrix (i.e., a matrix with both itself and its transpose being difference matrices) has some nice properties. Based on these findings, some new methods for constructing E (f NOD) -optimal SSDs via generalized Hadamard matrices are developed. Meanwhile, the non-orthogonality of the proposed designs is well controlled by the source designs. In addition, some generalized Hadamard matrices with nice properties are constructed for obtaining E (f NOD) -optimal SSDs. The proposed methods are easy to implement and many new SSDs can then be constructed. [ABSTRACT FROM AUTHOR]

An attractive type of space-filling design for computer experiments is the class of maximin distance designs. Algorithmic search is commonly used for finding such designs, but this approach becomes ineffective for large problems. Theoretical construction of maximin distance designs is challenging; some results have been obtained recently, often using highly specialized techniques. This article presents an easy-to-use method for constructing maximin distance designs. The method is versatile as it works with any distance measure. The basic idea is to construct large designs from small designs, and the method is effective because the quality of large designs is guaranteed by that of small designs, as evaluated by the maximin distance criterion. [ABSTRACT FROM AUTHOR]

Strong orthogonal arrays enjoy more attractive space-filling properties than ordinary orthogonal arrays for computer experiments. In this paper, we propose two methods for constructing column-orthogonal nearly strong orthogonal arrays. These designs enjoy column orthogonality, inherit the attractive two-dimensional space-filling property of strong orthogonal arrays, and can accommodate twice or more number of factors than the existing strong orthogonal arrays. In addition, the proposed designs with four levels enjoy an attractive space-filling property under the maximin distance criterion. The construction methods are convenient and flexible, and the resulting designs are useful in computer experiments. • The concept of column-orthogonal nearly strong orthogonal arrays is proposed. • Convenient and flexible construction methods are provided. • New designs have column-orthogonality, space-filling properties and more factors. [ABSTRACT FROM AUTHOR]

Many industrial experiments involve factors with levels more difficult to change or control than others, which leads to the development of two-level fractional factorial split-plot (FFSP) designs. Recently, mixed-level FFSP designs were proposed due to the requirement of different-level factors. In this paper, we generalize the Bayesian optimal criterion for mixed two- and four-level FFSP designs, and then provide Bayesian minimum aberration (MA) criterion to rank FFSP designs. Bayesian MA criterion can give a natural ordering for the effects involving two-level factors and three components of a four-level factor. We also discuss the relationship between the Bayesian optimal and Bayesian MA criteria. Furthermore, we consider the designs with both qualitative and quantitative factors. [ABSTRACT FROM AUTHOR]

Composite designs are frequently utilized for fitting response surfaces in practice. This paper proposes a new type of composite designs, orthogonal uniform composite designs (OUCDs), which combine orthogonal arrays and uniform designs. Such designs not only inherit the advantages of orthogonal-array composite designs such as high estimation efficiencies and ability for multiple analysis for cross validation, but also have more flexible run sizes than central composite designs and orthogonal-array composite designs. Moreover, OUCDs are more robust than other types of composite designs under certain conditions. Some construction methods for OUCDs under the maximin distance criterion are provided and their properties are also studied. It is shown that many constructed OUCDs are maximin distance designs. • Orthogonal uniform composite designs (OUCDs) have high estimation efficiencies. • OUCDs have more flexible run sizes than many types of composite designs. • OUCDs are robust than other types of composite designs. • Many constructed OUCDs are maximin distance designs. [ABSTRACT FROM AUTHOR]

Fractional factorial split-plot (FFSP) designs are often used when the levels of some factors are difficult to change or control. If not all experimental factors have the same number of levels, mixed-level designs are natural choices. This paper provides the necessary and sufficient conditions for mixed 2- and 2 r -level FFSP designs of resolution III or IV to contain clear main effects or two-factor interaction components. Particularly, the sufficient conditions are proved through constructing the corresponding designs. The new results here are more general and include Zhao and Chen (2012a,b)'s results as special cases for r = 2. • Conditions for some mixed-level FFSP designs with clear effects are provided. • The sufficient conditions are proved through constructing the corresponding designs. • The new results are more general and cover some existing results as special cases. [ABSTRACT FROM AUTHOR]

Drawing samples from a target distribution is essential for statistical computations when the analytical solution is infeasible. Many existing sampling methods may be easy to fall into the local mode or strongly depend on the proposal distribution when the target distribution is complicated. In this article, the Global Likelihood Sampler (GLS) is proposed to tackle these problems and the GL bootstrap is used to assess the Monte Carlo error. GLS takes the advantage of the randomly shifted low-discrepancy point set to sufficiently explore the structure of the target distribution. It is efficient for multimodal and high-dimensional distributions and easy to implement. It is shown that the empirical cumulative distribution function of the samples uniformly converges to the target distribution under some conditions. The convergence for the approximate sampling distribution of the sample mean based on the GL bootstrap is also obtained. Moreover, numerical experiments and a real application are conducted to show the effectiveness, robustness, and speediness of GLS compared with some common methods. It illustrates that GLS can be a competitive alternative to existing sampling methods. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Mixture experiments have attracted increasingly attention due to their great practical value in production and living, while uniform designs over irregular experimental regions have become a hot topic in the area of experimental designs in the past two decades. Noting that the experimental region of a mixture experiment withqcomponents under some constraints is in fact a (q− 1)-dimensional geometry, this article proposes a new method for searching nearly uniform designs for mixture experiments with any complex constraints. Two examples with some tables and figures are given to illustrate this method. [ABSTRACT FROM PUBLISHER]

In computer experiments, space-filling designs with a sliced structure or nested structure have received much recent interest and been studied separately. However, it is likely that designs with both structures are needed in some situations, but there are no suitable designs so far. In this paper, we construct a special class of nested Latin hypercube designs with sliced structures, in such a design, a small sliced Latin hypercube design is nested within a large one. The construction method is easy to implement and the number of factors is flexible. Numerical simulations show the usefulness of the newly proposed designs. [ABSTRACT FROM PUBLISHER]

Sliced Latin hypercube designs are useful for computer experiments with qualitative and quantitative factors, model calibration, cross validation, multi-level function estimation, stochastic optimization and data pooling. Orthogonality and second-order orthogonality are crucial in identifying important inputs. Besides orthogonality, good space-filling properties are also necessary for Latin hypercube designs. In this paper, a construction method for second-order orthogonal sliced Latin hypercube designs is proposed. The constructed designs are further optimized to achieve better space-filling properties. Furthermore, the method is extended to construct nearly orthogonal sliced Latin hypercube designs. The numbers of slices and columns as well as the levels of the resulting designs are more flexible than those obtained by existing methods. [ABSTRACT FROM AUTHOR]

Fourier-cosine models, rooted in the discrete cosine transformation, are widely used in numerous applications in science and engineering. Because the selection of design points where data are collected greatly affects the modeling process, we study the choice of fractional factorial designs for fitting Fourier-cosine models. We propose a new type of generalized resolution and provide a framework for the construction of fractional factorial designs with the maximum generalized resolution. The construction applies level permutations to regular designs with a novel nonlinear transformation. A series of theoretical results are developed to characterize the properties of the level-permuted designs. Based on the theory, we further provide efficient methods for constructing designs with high resolutions without any computer search. Examples are given to show the advantages of the constructed designs over existing ones. [ABSTRACT FROM AUTHOR]

Abstract: Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Inspired by the construction of cyclic orthogonal designs with prime power run numbers in Plackett and Burman (1946), a method for constructing optimal multi-level SSDs with cyclic structure is explored in this paper. Some newly constructed designs are tabulated for practical use. Meanwhile, some of the resulting designs are shown to be also optimal under the criterion. In addition, we show that a sufficient condition for a balanced mixed-level saturated design to be orthogonal is that the weighted coincidence number between any two distinct rows of this design is a constant. An easier proof for the orthogonality of the Plackett and Burman designs with prime power run numbers is also presented. [Copyright &y& Elsevier]

Abstract: Latin hypercube designs (LHDs) are widely used in computer experiments because of their one-dimensional uniformity and other properties. Recently, a number of methods have been proposed to construct LHDs with properties that all linear effects are mutually orthogonal and orthogonal to all second-order effects, i.e., quadratic effects and bilinear interactions. This paper focuses on the construction of LHDs with the above desirable properties under the Fourier-polynomial model. A convenient and flexible algorithm for constructing such orthogonal LHDs is provided. Most of the resulting designs have different run sizes from that of Butler (2001), and thus are new and very suitable for factor screening and building Fourier-polynomial models in computer experiments as discussed in Butler (2001). [Copyright &y& Elsevier]

Various optimal criteria have been proposed to rank asymmetrical fractional factorial designs. Among them, the generalized minimum aberration and the minimum moment aberration criteria are the most popular ones and have received much attention. Recently, Liu et al. (Stat Sin 16:1285-1297, 2006) proposed the minimum χ criterion in terms of level-combinations. In this paper, the equivalency of the generalized minimum aberration and the minimum χ criteria is reported, which not only provides another justification for each other but also develops some theoretical results for designs with generalized minimum aberration and some lower bounds for the generalized wordlength pattern. Besides, an analytic relationship between generalized minimum aberration and minimum moment aberration is obtained for asymmetrical fractional factorial designs. [ABSTRACT FROM AUTHOR]

Supersaturated designs (SSDs) have been highly valued in recent years for their ability of screening out important factors in the early stages of experiments. Recently, Liu and Lin (in Statist Sinica 19:197-211, 2009) proposed a method to construct optimal mixed-level SSDs from smaller multi-level SSDs and transposed orthogonal arrays (OAs). This paper extends their method to construct more equidistant optimal SSDs by replacing the multi-level SSDs and transposed OAs with mixed-level SSDs and general transposed difference matrices, respectively, and then proposes two practical methods for constructing weak equidistant SSDs based on this extended method. A large number of new optimal SSDs can be constructed from these three methods. Some examples are provided and more new designs are listed in 'Appendix' for practical use. [ABSTRACT FROM AUTHOR]

Abstract: Two designs are geometrically isomorphic if one design can be obtained from the other by reordering the runs, relabeling the factors and/or reversing the level order of one or more factors. In this paper, some new necessary and sufficient conditions for identifying geometric isomorphism of symmetric designs with prime levels are provided. A new algorithm for checking geometric isomorphism is proposed and a searching result for geometrically non-isomorphic 3-level orthogonal arrays of 18 runs is presented. [Copyright &y& Elsevier]

Abstract: Inspired by the ideas of column and row juxtaposition in and level transformation in , this paper presents a new method for constructing optimal supersaturated designs (SSDs). This method provides a convenient way to construct mixed-level designs with relatively large numbers of levels, avoiding the blind search and numerous calculations by computers. The goodness of the resulting SSDs is judged by the ( and ) and J 2 () criteria. Some nice properties of the new designs are also provided. [Copyright &y& Elsevier]

Abstract: Latin hypercube designs (LHDs) have recently found wide applications in computer experiments. A number of methods have been proposed to construct LHDs with orthogonality among main-effects. When second-order effects are present, it is desirable that an orthogonal LHD satisfies the property that the sum of elementwise products of any three columns (whether distinct or not) is 0. The orthogonal LHDs constructed by , , and all have this property. However, the run size n of any design in the former three references must be a power of two (n=2 c ) or a power of two plus one (n=2 c +1), which is a rather severe restriction. In this paper, we construct orthogonal LHDs with more flexible run sizes which also have the property that the sum of elementwise product of any three columns is 0. Further, we compare the proposed designs with some existing orthogonal LHDs, and prove that any orthogonal LHD with this property, including the proposed orthogonal LHD, is optimal in the sense of having the minimum values of ave(|t|), t max, ave(|q|) and q max. [Copyright &y& Elsevier]

Abstract: A factorial design can be uniquely determined by an indicator function which is constructed by means of orthogonal contrasts. Since the orthogonal contrasts are not unique, invariant measures are preferred. However, some particular orthogonal contrasts may express more information about designs than the others and be worth our attention. In this paper, a kind of indicator function based on orthogonal complex contrasts is introduced to represent general factorial designs and its significance on projection designs is presented. Based on this function, a generalized resolution and a new aberration criterion are developed to rank combinatorially non-isomorphic designs with prime levels. Some results and comparison are provided by means of examples. [Copyright &y& Elsevier]

Fractional factorial split-plot (FFSP) designs have received much attention in recent years. In this article, the matrix representation for FFSP designs with multi-level factors is first developed, which is an extension of the one proposed by Bingham and Sitter (1999b) for the two-level case. Based on this representation, periodicity results of maximum resolution and minimum aberration for such designs are derived. Differences between FFSP designs with multi-level factors and those with two-level factors are highlighted. [ABSTRACT FROM AUTHOR]

Abstract: Factorial designs are arguably the most widely used designs in scientific investigations. Generalized minimum aberration (GMA) and uniformity are two important criteria for evaluating both regular and non-regular designs. The generation of GMA designs is a non-trivial problem due to the sequential optimization nature of the criterion. Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem. Moreover, many new designs with GMA or near-GMA are reported, which are also (nearly) optimal under the uniformity measure. [Copyright &y& Elsevier]

Abstract: Supersaturated designs (SSDs) offer a potentially useful way to investigate many factors with only few experiments in the preliminary stages of experimentation. This paper explores how to construct -optimal mixed-level SSDs using k-cyclic generators. The necessary and sufficient conditions for the existence of mixed-level k-circulant SSDs with the equal occurrence property are provided. Properties of the mixed-level k-circulant SSDs are investigated, in particular, the sufficient condition under which the generator vector produces an -optimal SSD is obtained. Moreover, many new -optimal mixed-level SSDs are constructed and listed. The method here generalizes the one proposed by Liu and Dean [2004. -circulant supersaturated designs. Technometrics 46, 32–43] for two-level SSDs and the one due to Georgiou and Koukouvinos [2006. Multi-level k-circulant supersaturated designs. Metrika 64, 209–220] for the multi-level case. [Copyright &y& Elsevier]

Clear effects criterion is one of the most important rules for selecting 2 m - p designs, and it is valuable to know the maximum number of clear two-factor interactions in 2 m - p designs. This article provides lower bounds on the maximum number of clear two-factor interactions for and designs by constructing specific designs, respectively. The lower bounds improve the ones given in Tang et al. (2002) and the construction methods perform quite well. [ABSTRACT FROM AUTHOR]

Computer experiments play a crucial role when physical experiments are expensive or difficult to be carried out. As a kind of designs for computer experiments, maximin distance designs have been widely studied. Many existing methods for obtaining maximin distance designs are based on stochastic algorithms, and these methods will be infeasible when the run size or number of factors is large. In this paper, we propose some deterministic construction methods for maximin L 2 -distance designs in two to five dimensions based on densest packings. The resulting designs have large L 2 -distances and are mirror-symmetric. Some of them have the same L 2 -distances as the existing optimal maximin distance designs, and some of the others are completely new. Especially, the resulting 2-dimensional designs possess a good projection property. [ABSTRACT FROM AUTHOR]

For designs of computer experiments, column-orthogonality and space-filling property are two desirable properties. In this paper, we develop methods for constructing a new class of designs that include orthogonal Latin hypercube designs as special cases. These designs are not only column-orthogonal but also have good space-filling properties in low dimensions. All these appealing properties make them good choices for designing computer experiments. Based on orthogonal arrays, the proposed methods are easy to operate and flexible. Many new orthogonal designs with desirable space-filling properties are constructed and tabulated. Rotation matrices play a key role in the construction. • A new class of space-filling orthogonal designs is proposed. • Convenient and flexible construction methods are provided. • New designs possess attractive two- and three-dimensional space-filling properties. [ABSTRACT FROM AUTHOR]

The order-of-addition experiment aims at determining the optimal order of adding components such that the response of interest is optimized. Order of addition has been widely involved in many areas, including bio-chemistry, food science, nutritional science, pharmaceutical science, etc. However, such an important study is rather primitive in statistical literature. In this paper, a thorough study on pair-wise ordering designs for order of addition is provided. The recursive relation between two successive full pair-wise ordering designs is developed. Based on this recursive relation, the full pair-wise ordering design can be obtained without evaluating all the orders of components. The value of the D-efficiency for the full pair-wise ordering model is then derived. It provides a benchmark for choosing the fractional pair-wise ordering designs. To overcome the unaffordability of the full pair-wise ordering design, a new class of minimal-point pair-wise ordering designs is proposed. A job scheduling problem as well as simulation studies are conducted to illustrate the performance of the pair-wise ordering designs for determining the optimal orders. It is shown that the proposed designs are very efficient in determining the optimal order of addition. [ABSTRACT FROM AUTHOR]

The fractional factorial split-plot (FFSP) design is an important experimental design both in theory and in practice. There is extensive literature on the two-level FFSP design and its various variants. However, there is little work on the s-level FFSP design and its variants in the asymmetrical (i.e., mixed-level) case, where s is any prime or prime power. Such designs are commonly used e.g. in agriculture, medicine and chemistry. This paper provides the necessary and sufficient conditions for the existence of resolution III or IV regular s (n 1 + n 2) - (k 1 + k 2) (s r) designs which contain clear main effects or two-factor interaction components. In particular, the sufficient conditions are proved through constructing the corresponding designs, and some examples are provided to illustrate the construction methods. [ABSTRACT FROM AUTHOR]

Maximin distance Latin hypercube designs (LHDs) are extensively applied in computer experiments, but it is challenging to construct such designs. In this paper, based on a 2 2 full factorial design and a series of saturated two-level regular designs, a number of maximin distance LHDs are constructed via the rotation method. Some of the constructed LHDs are exactly optimal and the others are asymptotically optimal under the maximin L 2 -distance criterion. The constructed maximin distance LHDs have two prominent advantages: (i) no computer search is needed; and (ii) they are orthogonal or nearly orthogonal. Detailed comparisons with existing LHDs show that the constructed LHDs have larger minimum distances between design points. • Maximin distance Latin hypercube designs are constructed via the rotation method. • The resulting designs are orthogonal or nearly orthogonal. • The methods are efficient for constructing large designs with no computer search. [ABSTRACT FROM AUTHOR]

Abstract Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and machine learning. For example, it produces reasonable solutions for problems in sensitivity analysis, local model explanation toward the interpretable machine learning, node importance in social network, attribution models, etc. However, it could be very expensive to compute the Shapley value. Specifically, in a d-player coalition game, calculating a Shapley value requires the evaluation of d ! or 2 d marginal contribution values, depending on whether we are taking the permutation or combination formulation of the Shapley value. Hence, it becomes infeasible to calculate the Shapley value when d is reasonably large. A common remedy is to take a random sample of the permutations to surrogate for the complete list of permutations. We find an advanced sampling scheme can be designed to yield much more accurate estimation of the Shapley value than the simple random sampling (SRS). Our sampling scheme is based on combinatorial structures in the field of design of experiments (DOE), particularly the order-of-addition experimental designs for the study of how the orderings of components would affect the output. We show that the obtained estimates are unbiased, and can sometimes deterministically recover the original Shapley value. Both theoretical and simulations results show that our DOE-based sampling scheme outperforms SRS in terms of estimation accuracy. Surprisingly, it is also slightly faster than SRS. Lastly, real data analysis is conducted for the C. elegans nervous system and the 9/11 terrorist network. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Abstract The spread of COVID-19 makes it essential to investigate its prevalence. In such investigation research, as far as we know, the widely-used sampling methods didn’t use the information sufficiently about the numbers of the previously diagnosed cases, which provides a priori information about the true numbers of infections. This motivates us to develop a new, two-stage sampling method in this paper, which utilizes the information about the distributions of both population and diagnosed cases, to investigate the prevalence more efficiently. The global likelihood sampling, a robust and efficient sampler to draw samples from any probability density function, is used in our sampling strategy, and thus, our new method can automatically adapt to the complicated distributions of population and diagnosed cases. Moreover, the corresponding estimating method is simple, which facilitates the practical implementation. Some recommendations for practical implementation are given. Finally, several simulations and a practical example verify its efficiency. [ABSTRACT FROM AUTHOR]

Abstract Initial screening experiments often leave some problems unresolved, adding follow-up runs is needed to clarify the initial results. In this paper, a technique is developed to add additional experimental runs to an initial supersaturated design. The added runs are generated with respect to the Bayesian D s -optimality criterion and the procedure can incorporate the model information from the initial design. After analysis of the initial experiment with several methods, factors are classified into three groups: primary, secondary, and potential according to the times that they have been identified. The focus is on those secondary factors since they have been identified several times but not so many that experimenters are sure that they are active, the proposed Bayesian D s -optimal augmented design would minimize the error variances of the parameter estimators of secondary factors. In addition, a blocking factor will be involved to describe the mean shift between two stages. Simulation results show that the method performs very well in certain settings. Highlights • Bayesian D s -optimal augmented SSD uses initial-design info to plan follow-up runs. • The factor classification is determined by multiple analysis methods. • The new method considers the shift in average responses between the two experiments. • The Bayesian D s -optimality performs better in certain situations. [ABSTRACT FROM AUTHOR]

Missing observations can hardly be avoided even by a well-planned experiment. Based on the orthogonal-array based composite designs proposed by Xu et al. (2014), new orthogonal-array based composite minimax loss designs are constructed. Comparisons between the proposed designs and other composite designs, including orthogonal-array based composite designs, augmented pairs designs, augmented pairs minimax loss designs, central composite designs, and small composite designs are made in detail, which show that the new composite designs are more robust to one missing design point in terms of the D -efficiency and generalized scaled standard deviation. Moreover, it is demonstrated that the D -efficiency remains unchanged for both level permutation and column permutation in some special cases. [ABSTRACT FROM AUTHOR]

Follow-up experimental designs are popularly used in industry. In practice, some important factors may be neglected for various reasons in the first-stage experiment and they need to be added in the next stage. In this paper, we propose a method for augmenting supersaturated designs with newly added factors and augmented levels using the Bayesian D-optimality criterion. In addition, we suggest using the integrated Bayesian D-optimal augmented design to plan the follow-up experiment when the newly added factors have been allowed to vary in an appropriate region. Examples and simulation results show that the augmented designs perform well in improving identified rates of latent factor effects. [ABSTRACT FROM AUTHOR]

Good lattice point sets have desirable space-filling properties, and many designs with large L 1 -distance can be obtained by the leave-one-out good lattice point method (Zhou and Xu, 2015). However, there are negatively fully correlated columns in such a design. This is undesirable in the modeling of computer experiments. To overcome such a deficiency, we propose a class of designs based on the leave-one-out good lattice point method, whose columns can be divided into two groups, such that any two columns are column-orthogonal when they are from different groups and nearly column-orthogonal when they are in the same group. The new designs can also estimate the linear effects without being correlated with the second-order effects. Moreover, they have good stratification properties and their L 1 -distances are comparable with the corresponding designs in Zhou and Xu (2015). [ABSTRACT FROM AUTHOR]

The stochastic search variable selection proposed by George and McCulloch (J Am Stat Assoc 88:881-889, 1993) is one of the most popular variable selection methods for linear regression models. Many efforts have been proposed in the literature to improve its computational efficiency. However, most of these efforts change its original Bayesian formulation, thus the comparisons are not fair. This work focuses on how to improve the computational efficiency of the stochastic search variable selection, but remains its original Bayesian formulation unchanged. The improvement is achieved by developing a new Gibbs sampling scheme different from that of George and McCulloch (J Am Stat Assoc 88:881-889, 1993). A remarkable feature of the proposed Gibbs sampling scheme is that, it samples the regression coefficients from their posterior distributions in a componentwise manner, so that the expensive computation of the inverse of the information matrix, which is involved in the algorithm of George and McCulloch (J Am Stat Assoc 88:881-889, 1993), can be avoided. Moreover, since the original Bayesian formulation remains unchanged, the stochastic search variable selection using the proposed Gibbs sampling scheme shall be as efficient as that of George and McCulloch (J Am Stat Assoc 88:881-889, 1993) in terms of assigning large probabilities to those promising models. Some numerical results support these findings. [ABSTRACT FROM AUTHOR]

Computer experiments have received a great deal of attention in many fields of science and technology. Most literature assumes that all the input variables are quantitative. However, researchers often encounter computer experiments involving both qualitative and quantitative variables (BQQV). In this article, a new interface on design and analysis for computer experiments with BQQV is proposed. The new designs are one kind of sliced Latin hypercube designs with points clustered in the design region and possess good uniformity for each slice. For computer experiments with BQQV, such designs help to measure the similarities among responses of different level-combinations in the qualitative variables. An adaptive analysis strategy intended for the proposed designs is developed. The proposed strategy allows us to automatically extract information from useful auxiliary responses to increase the precision of prediction for the target response. The interface between the proposed design and the analysis strategy is demonstrated to be effective via simulation and a real-life example from the food engineering literature. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Supersaturated design (SSD) plays an important role in screening factors. E (f N O D) criterion is one of the most widely used criteria to evaluate multi-level and mixed-level SSDs. This paper provides some methods to construct multi-level E (f N O D) optimal SSDs with general run sizes, which can also be extended to construct mixed-level SSDs. The main idea of these methods is combining two processed generalized Hadamard matrices with the expansive replacement method. These proposed methods are easy to perform. Besides, the non-orthogonality between any two columns of the resulting SSDs is well controlled by that of the source designs. Some illustrative examples are given and several new SSDs are provided in this paper. • Convenient and flexible construction methods are provided. • Many new E (f N O D) optimal supersaturated designs are constructed. • Non-orthogonality of the new designs is well controlled by that of the source designs. [ABSTRACT FROM AUTHOR]

Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the experiment is relatively large. Suitably partitioning inhomogeneous units into homogeneous groups, known as blocks, is a practical design strategy. How to partition the experimental units for a given design is an important issue. The blocked general minimum lower order confounding is a new criterion for selecting blocked designs. With the help of doubling theory and second order saturated design, we present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion. [ABSTRACT FROM AUTHOR]

The Latin hypercube design (LHD) is a popular choice of experimental design when computer simulation is used to study a physical process. In this paper, we propose some methods for constructing nearly orthogonal Latin hypercube designs (NOLHDs) with 2, 4, 8, 12, 16, 20 and 24 factors having flexible run sizes. These designs can be very useful when orthogonal Latin hypercube designs (OLHDs) of the needed sizes do not exist. [ABSTRACT FROM AUTHOR]

U-type designs and orthogonal Latin hypercube designs (OLHDs) have been used extensively for performing computer experiments. Both have good spaced filling properties in one-dimension. U-type designs may not have low correlations among the main effects, quadratic effects and two-factor interactions. On the other hand, OLHDs are hard to be found due to their large number of levels for each factor. Recently, alternative classes of U-type designs with zero or low correlations among the effects of interest appear in the literature. In this paper, we present new classes of U-type or quantitative $$3$$ -orthogonal designs for computer experiments. The proposed designs are constructed by combining known combinatorial structures and they have their main effects pairwise orthogonal, orthogonal to the mean effect, and orthogonal to both quadratic effects and two-factor interactions. [ABSTRACT FROM AUTHOR]