B. N. Mandal

IPPS Sampling Plans Excluding Adjacent Units

The concept of inclusion probability proportional to size sampling plans excluding adjacent units separated by at most a distance of m (≥ 1) units {IPPSEA plans} is introduced. IPPSEA plans ensure that the first-order inclusion probabilities of units are proportional to size measures of the units, while the second-order inclusion probabilities are zero for pairs of adjacent units separated by a distance of m units or less. IPPSEA plans have been obtained by making use of binary, proper, and unequireplicated block designs and linear programing approach. The performance of IPPSEA plans using Horvitz–Thompson estimator of population total has been compared with existing sampling plans such as simple random sampling without replacement (SRSWOR), balanced sampling plans excluding adjacent units {BSA (m) plans}, probability proportional to size with replacement, Hartley and Raos plan (1962), Rao et al.s strategy (1962), and Sampfords IPPS plan (1967) using a real life population. Unbiased estimation of Horvitz–Thompson estimator of population total is not possible in these types of plans because some of the second-order inclusion probabilities are zero. To resolve this problem, one approximate variance estimation technique has been suggested.

Statistical Approaches for Gene Selection, Hub Gene Identification and Module Interaction in Gene Co-Expression Network Analysis: An Application to Aluminum Stress in Soybean (Glycine max L.).

Selection of informative genes is an important problem in gene expression studies. The small sample size and the large number of genes in gene expression data make the selection process complex. Further, the selected informative genes may act as a vital input for gene co-expression network analysis. Moreover, the identification of hub genes and module interactions in gene co-expression networks is yet to be fully explored. This paper presents a statistically sound gene selection technique based on support vector machine algorithm for selecting informative genes from high dimensional gene expression data. Also, an attempt has been made to develop a statistical approach for identification of hub genes in the gene co-expression network. Besides, a differential hub gene analysis approach has also been developed to group the identified hub genes into various groups based on their gene connectivity in a case vs. control study. Based on this proposed approach, an R package, i.e., dhga (https://cran.r-project.org/web/packages/dhga) has been developed. The comparative performance of the proposed gene selection technique as well as hub gene identification approach was evaluated on three different crop microarray datasets. The proposed gene selection technique outperformed most of the existing techniques for selecting robust set of informative genes. Based on the proposed hub gene identification approach, a few number of hub genes were identified as compared to the existing approach, which is in accordance with the principle of scale free property of real networks. In this study, some key genes along with their Arabidopsis orthologs has been reported, which can be used for Aluminum toxic stress response engineering in soybean. The functional analysis of various selected key genes revealed the underlying molecular mechanisms of Aluminum toxic stress response in soybean.

Efficient Incomplete Block Designs Through Linear Integer Programming

SYNOPTIC ABSTRACT The purpose of this paper is to present a linear integer programming approach to construct efficient binary incomplete block designs for any given number of treatments v, number of blocks b, with common block-size k, and with a nearly balanced concurrence matrix. The proposed approach is illustrated by constructing an efficient incomplete block design. A-efficient and D-efficient incomplete block designs have been constructed and catalogued using the proposed algorithm for a restricted range of parameters 3 ⩽ v ⩽ 20, b ⩾ v, and 2 ⩽ k ⩽ min(10, v − 1), with vb⩽1, 000. An R package is developed to implement the proposed approach.

Construction of Efficient Mixed-Level k-Circulant Supersaturated Designs

An algorithm to construct efficient balanced mixed-level k-circulant supersaturated designs with m factors and n runs is presented in this article. The algorithm generates efficient mixed-level k-circulant supersaturated designs very fast. Using the proposed algorithm many mixed-level, balanced supersaturated designs are constructed and catalogued. A list of many optimal and near optimal, mixed-level supersaturated designs is also provided for m ∤ 60.

Incomplete row-column designs with factorial treatment structure for estimating main effects with full efficiency

ABSTRACT In this paper, we propose two methods of constructing row-column designs for factorial experiments. The constructed designs have orthogonal factorial structure with balance and permits estimation of main effects with full efficiency.

Two-dimensional balanced sampling plans excluding adjacent units under sharing a border and island adjacency schemes

ABSTRACT In Balanced Sampling Plans Excluding Adjacent Units (BSA plans) first order inclusion probabilities are equal and second order inclusion probabilities are zero for pairs of units at a distance less than or equal to m and are constant for pairs of units which are at a distance greater than m. These plans are useful when the adjacent units in the population provide similar information. In this paper, an algorithm based on linear programming approach has been developed for construction of two-dimensional BSA plans under sharing a border and island adjacency schemes for m ≤ 2. Some results on existence of such BSA plans have also been obtained for each adjacency scheme separately.

On balanced incomplete Latin square designs

ABSTRACT Recently, balanced incomplete Latin square designs are introduced in the literature. We propose three methods of constructions of balanced incomplete Latin square designs. Particular classes of Latin squares namely Knut Vik designs, semi Knut Vik designs, and crisscross Latin squares play a key role in the construction.

Balanced treatment incomplete block designs through integer programming

ABSTRACT An algorithm is presented to construct balanced treatment incomplete block (BTIB) designs using a linear integer programming approach. Construction of BTIB designs using the proposed approach is illustrated with an example. A list of efficient BTIB designs for 2 ⩽ v ⩽ 12, v + 1 ⩽ b ⩽ 50, 2 ⩽ k ⩽ min(10, v), r ⩽ 10, r0 ⩽ 20 is provided. The proposed algorithm is implemented as part of an R package.

Cyclic circular balanced and strongly balanced crossover designs through integer programming

ABSTRACT This article proposes a new linear integer programming approach to obtain cyclic circular balanced and strongly balanced crossover designs for a given number of treatments v, number of periods p, and number of units n. The linear integer programming approach has been used for generating a sequence of treatments to be assigned to the units. Using this approach, cyclic circular balanced and strongly balanced crossover designs for v < 30, p < 5, and λ ⩽ 4 or λ* ⩽ 4 have been generated, where λ (λ*) refers to the number of times each treatment is preceded by every other treatment excluding itself (including itself) depending on whether it is circular balanced or circular strongly balanced. The designs obtained are uniform over periods. A catalogue of designs for v < 30, p < 5, λ ⩽ 4 or λ* ⩽ 4, p < v with n ⩽ 100 is given. The designs obtained are universally optimal over the class of all connected designs with a fixed number of treatments, number of periods, and number of sequences.