Searching probabilities for nonzero effects in search designs for the noisy case

Shirakura, Teruhiro; Takahashi, Tadashi; Srivastava, J. N.

doi:10.1214/aos/1032181169

Cited by 29 publications

(27 citation statements)

References 5 publications

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“…Later, Shirakura, Takahashi, and Srivastava (1996) went on to examine the "probability of correct search" and its use in comparing search designs in the noisy case. They gave an explicit formula for the probability of correct selection of k = 1 non-zero effect from β 2 when the errors follow a N (0, σ 2 ) distribution, and calculated this probability for two examples for different values of the "signal to noise" ratio ρ = β 21 /σ (where β 21 is the true value of the non-zero effect from β 2 ).…”

Section: Identifying the Non-zero Effectsmentioning

confidence: 99%

“…The probabilities are remarkably high; above 0.95 for (i) with 5-10 factors and ρ > 1.5, and just a little lower for (ii) where the search is more competitive. Ghosh and Teschmacher (2002) proposed two criteria based on probabilities of correct search, in addition to that of Shirakura et al (1996), for determining which of several designs is more likely to identify the k = 1 non-zero interaction. That paper also generalized the three criteria for all values of ρ so that comparison of search designs can be made without requiring ρ to be known.…”

Section: Identifying the Non-zero Effectsmentioning

confidence: 99%

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J.N. Srivastava and experimental design

Ghosh

Dean

2014

Journal of Statistical Planning and Inference

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J. N. Srivastava was a tremendously productive statistical researcher for five decades. He made significant contributions in many areas of statistics, including multivariate analysis and sampling theory. A constant throughout his career was the attention he gave to problems in discrete experimental design, where many of his best known publications are found. This paper focuses on his design work, tracing its progression, recounting his key contributions and ideas, and assessing its continuing impact. A synopsis of his design-related editorial and organizational roles is also included.MSC 2000 subject classification. 62K15.

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Section: Identifying the Non-zero Effectsmentioning

confidence: 99%

Section: Identifying the Non-zero Effectsmentioning

confidence: 99%

J.N. Srivastava and experimental design

Ghosh

Dean

2014

Journal of Statistical Planning and Inference

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“…Katona and Srivastava [41] lay a mathematical foundation for this in the binary case. Subsequently, there has been substantial research on these search designs; see, for example, [31,32,66]. While this research does introduce the notion of location, it is in addition to the measurement afforded by a usual factorial design, and hence asks for stronger properties than we require.…”

Section: Effect Aliasingmentioning

confidence: 99%

Locating and detecting arrays for interaction faults

2007

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The identification of interaction faults in component-based systems has focussed on indicating the presence of faults, rather than their location and magnitude. While this is a valuable step in screening a system for interaction faults prior to its release, it provides little information to assist in the correction of such faults. Consequently tests to reveal the location of interaction faults are of interest. The problem of nonadaptive location of interaction faults is formalized under the hypothesis that the system contains (at most) some number d of faults, each involving (at most) some number t of interacting factors. Restrictions on the number and size of the putative faults lead to numerous variants of the basic problem. The relationships between this class of problems and interaction testing using covering arrays to indicate the presence of faults, designed experiments to measure and model faults, and combinatorial group testing to locate faults in a more general testing scenario, are all examined. While each has some definite similarities with the fault location problems for componentbased systems, each has some striking differences as well. In this paper, we formulate the combinatorial problems for locating and detecting arrays to undertake interaction fault location. Necessary conditions for existence are established, and using a close connection to covering arrays, asymptotic bounds on the size of minimal locating and detecting arrays are established.

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“…Many researchers have done work on designs for discriminating between two or more competing models; Atkinson and Cox (1974); Atkinson and Fedorov (1975a and b); Srivastava (1975Srivastava ( , 1977; Srivastava and Mallenby (1985); Pukelsheim and Rosenberger (1993); Dette (1994); Shirakura et al (1996); Biswas and Chaudhuri (2002); Ghosh and Teschmacher (2002); Dette and Kwiecien (2004); Ghosh and Tian (2006), and numerous others. In this paper we present new criterion functions for discriminating between two competing models.…”

Section: Introductionmentioning

confidence: 99%

Design and Inference for Discriminating between Two Competing Linear Regression Models

Ghosh

López–Fidalgo

Pal

2009

JJSS

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The problem of discriminating between two competing simple linear regression models MI and MII is discussed in this paper. Model MI is nested within model MII with a common linear term being present in both models with respect to an explanatory variable and an additional quadratic term with respect to the same explanatory variable being present in MII. The first criterion function for discrimination between MI and MII is in terms of minimizing the variance of the least squares estimated coefficient of the quadratic term. A lower bound is obtained for this variance. Two designs are presented satisfying this lower bound in two experimental regions. New criterion functions for discriminating between MI and MII are given based on maximizing the difference between the fitted values of n observations under MI and MII, and maximizing the difference between the predicted values under MI and MII. Several results are obtained for demonstrating the performances of these designs under two new criterion functions. We also present five general classes of designs and demonstrate their sharp relative performances with respect to our criterion functions. Some results for discriminating between two competing general linear models M III and MIV are also given.

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Searching probabilities for nonzero effects in search designs for the noisy case

Cited by 29 publications

References 5 publications

J.N. Srivastava and experimental design

J.N. Srivastava and experimental design

Locating and detecting arrays for interaction faults

Design and Inference for Discriminating between Two Competing Linear Regression Models

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