Constructions and Combinatorial Problems in Design of Experiments

Raghavarao, Damaraju; Searle, S. R.

doi:10.2307/3151174

Cited by 102 publications

(165 citation statements)

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“…It is known (Du and Hwang 2000) that the existence of d > 1 arrays of size m × m is equivalent to the existence of 2(d − 1) of mutually orthogonal Latin squares (Beth et al 1999) of order m. Accordingly, an affine plane of order q can be used to produce up to q/2 arrays of size q × q satisfying unique collinearity (Raghavarao 1971). For completeness' sake, we describe here such a design in detail.…”

Section: Transversal Designsmentioning

confidence: 99%

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Pooled Genomic Indexing (PGI): Analysis and Design of Experiments

Csűrös

Milosavljevic

2004

Journal of Computational Biology

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Pooled Genomic Indexing (PGI) is a novel method for physical mapping of clones onto known sequences. PGI is carried out by pooling arrayed clones, and generating shotgun sequence reads from the pools. The shotgun sequences are compared to a reference sequence. In the simplest case clones are placed on an array and are pooled by rows and columns. If a shotgun sequence from a row pool and another shotgun sequence from a column pool match the reference sequence at a close distance, they are both assigned to the clone at the intersection of the two pools. Accordingly, the clone is mapped onto the region of the reference sequence between the two matches. A probabilistic model for PGI is developed, and several pooling designs are described and analyzed, including transversal designs and designs from linear codes. The probabilistic model and the pooling schemes are validated in simulated experiments where 625 rat BAC clones and 207 mouse BAC clones are mapped onto homologous human sequence.

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Section: Transversal Designsmentioning

confidence: 99%

“…Many group testing techniques (Raghavarao 1971;Du and Hwang 2000) are also applicable to the construction of pooling designs. The main advantage of pooling designs is the reduced cost of experiments, but when comparing pooling designs, other features may also need to be considered.…”

Section: Comparison Of Pooling Designsmentioning

confidence: 99%

Pooled Genomic Indexing (PGI): Analysis and Design of Experiments

Csűrös

Milosavljevic

2004

Journal of Computational Biology

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“…The L matrix is thus singular and noninvertible; hence, its generalized inverse is usually sought. Raghavarao [19], as well as Onukogu and Chigbu [14]; the generalized inverse matrix plays an important role in linear algebra in determining the solutions of linear equations when the coefficient matrix has no inverse; see, for example, Searle [21], Penrose [16] and Greville [12].…”

Section: Preliminariesmentioning

confidence: 99%

Application of Adjacency and Generalized Inverse Matrices to Ordering the Three Optimal (4 × 4)/ 4 Semi-Latin Squares

2016

Jour. Stat. Adv. Theory and Appl.

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In this work, we present the adjacency and generalized inverse matrices of the three optimal ( ) 4 4 4 × semi-Latin squares. These matrices are then used in conjunction with each other to discriminate amongst the squares by computing and comparing the variance of adjacency induced by the treatments in each square with those of the other squares, with the aid of MATLAB. The square which minimizes both the maximum variance of adjacency and the number of distinct values of the variance of adjacency amongst the squares, and where tie occurs, also have a minimum value of this variance is considered most N. P. UTO and P.

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“…For further explanation of how combinatorial design problems arise from statistically designed experiments, see [22,33,177,202].…”

Section: Example 14mentioning

confidence: 99%

Relations among partitions

Bailey¹

2017

Surveys in Combinatorics 2017

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Combinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments; it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.

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Constructions and Combinatorial Problems in Design of Experiments

Cited by 102 publications

References 0 publications

Pooled Genomic Indexing (PGI): Analysis and Design of Experiments

Pooled Genomic Indexing (PGI): Analysis and Design of Experiments

Application of Adjacency and Generalized Inverse Matrices to Ordering the Three Optimal (4 × 4)/ 4 Semi-Latin Squares

Relations among partitions

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