15 Spatial experimental design

Martin, R. J.

doi:10.1016/s0169-7161(96)13017-0

Cited by 25 publications

(4 citation statements)

References 73 publications

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“…Cambanis,46 Matern,47 Der Megreditchian,48 Micchelli and Wahba49 develop various aspects of optimal spatial allocations. Summaries of results in that area can be found in the studies of Fedorov,50 Guttorp et al 51 and Martin 52…”

Section: Evolution Of Optimal Designmentioning

confidence: 99%

Optimal experimental design

Fedorov

2010

WIREs Computational Stats

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estimators). He found that the points of the optimum design lie on the least ellipsoid which contains the design region, an insight further developed by Silvey and Titterington. 4 Guest 5 shows that, for the G-optimal design for the polynomial of order m, support points are roots of the derivatives of the (m − 1)th Legendre polynomial plus end points. Hoel 6 constructed D-optimal designs and commented that his designs are same as those of Guest. Two years later, Kiefer and Wolfowitz 7,8 proved the equivalence of G-and D-optimality and have started to treat experimental design as a particular area of convex optimization theory on the space of probability measures. The later direction is explored by Karlin and Studden 9 and by Fedorov. 10,11 Chernoff 12,13 went beyond the linear regression introducing locally optimal designs. Box and Lucas 14 use some of his ideas to find locally D-optimum designs for the single response of nonlinear models arising in chemical kinetics. Box and Hunter 15 develop an adaptive strategy in the Bayesian setting for updating the design one trial at a time as observations become available. Closely related approach based on the use of the Shannon information measure was initiated by Lindley 16 and elaborated by Fedorov and Pázman, 17 Caselton and Zidek, 18 Caselton et al. 19 , and recently revisited by Sebastiani and Wynn. 20 More on design for nonlinear models mainly in the Bayesian setting can be found in the studies of Ermakov, 21 Pilz, 22 Chaloner and Verdinelli. 23 Box and Hunter 15 show that an observation added at the point, where the variance of prediction using the linearized model is a maximum, is the most informative in the D-criterion sense. It is a short step to consider the same adaptive design generation for linear models, into which the parameter values do not enter, and so to obtain the (first order) algorithm for the iterative construction; see Fedorov, 11 Wynn,24 Fedorov and Malyutov. 25 These results evolved, cf., for instance, Atwood, 26 Fedorov and Uspensky, 27Vo lu me 2,

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Section: Evolution Of Optimal Designmentioning

confidence: 99%

Optimal experimental design

Fedorov

2010

WIREs Computational Stats

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“…Note that and competition models [cf. Martin (1996)l. However, more frequently only some historical data are available to construct and estimate the covariance matrix C.…”

Section: Correlated Observationsmentioning

confidence: 99%

Analysis and monitoring design for networks

Fedorov¹,

Flanagan²,

Rowan³

et al. 1998

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Experimental designs for the multi-host case of the network (4. 5) example. .. .. . Experimental designs with u2(z) = xTx for single-host case network (4,5). .. .. .. Experimental designs with 02(x) = xTx for multi-host case of network (4.5). .. .. . Experimental designs for the two-host case of network (8.12). 02(x) = 1. .. .. .. . Experimental designs for the two-host case of network (8.12). 02(x) = xTx. .. .. .

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“…Other methods based on spline function have been demonstrated to be e cient in modeling spatial variation in eld experiments (Verbyla et al, 1999;Velazco et al, 2017;Verbyla et al, 2018;Piepho et al, 2022). Detailed reviews of methods for spatial modeling can be found in Martin (1996), Hinkelmann and Kempthorne (2007) and Piepho et al (2008). Note that spatial models use information from neighbor observations in order to control environmental variation in the experiments; this needs to be differentiated from the genetic effect of neighbors that, for example, may occur by competition or differential exposure to diseases (Costa e Silva et al, 2017; Marjanovic et al, 2018;Marjanovic et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Genomic prediction for root and yield traits of barley under a water availability gradient. A case study comparing different spatial adjustments

Tessema,

Raffo,

Guo

et al. 2023

Preprint

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Background In drought periods, water use efficiency depends on the capacity of roots to extract water from deep soil. A semi-field phenotyping facility (RadiMax) was used to investigate above-ground and root traits in spring barley when grown under a water availability gradient. Above-ground traits included grain yield, grain protein concentration, grain nitrogen removal, and thousand kernel weight. Root traits were obtained through digital images measuring the root length at different depths. Two nearest-neighbor adjustments (M1 and M2) to model spatial variation were used for genetic parameter estimation and genomic prediction (GP). M1 and M2 used (co)variance structures and differed in the distance function to calculate between-neighbor correlations. M2 was the most developed adjustment, as accounted by the Euclidean distance between neighbors. Results The estimated heritabilities (\({\widehat{h}}^{2}\)) ranged from low to medium for root and above-ground traits. The genetic coefficient of variation (\(GCV\)) ranged from 3.2 to 7.0% for above-ground and 4.7 to 10.4% for root traits, indicating good breeding potential for the measured traits. The highest \(GCV\) observed for root traits revealed that significant genetic change in root development can be achieved through selection. We studied the genotype-by-water availability interaction, but no relevant interaction effects were detected. GP was assessed using leave-one-line-out (LOO) cross-validation. The predictive ability (PA) estimated as the correlation between phenotypes corrected by fixed effects and genomic estimated breeding values ranged from 0.33 to 0.49 for above-ground and 0.15 to 0.27 for root traits, and no substantial variance inflation in predicted genetic effects was observed. Significant differences in PA were observed in favor of M2. Conclusions The significant \(GCV\) and the accurate prediction of breeding values for above-ground and root traits revealed that developing genetically superior barley lines with improved root systems is possible. In addition, we found significant spatial variation in the experiment, highlighting the relevance of correctly accounting for spatial effects in statistical models. In this sense, the proposed nearest-neighbor adjustments are flexible approaches in terms of assumptions that can be useful for semi-field or field experiments.

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15 Spatial experimental design

Cited by 25 publications

References 73 publications

Optimal experimental design

Optimal experimental design

Analysis and monitoring design for networks

Genomic prediction for root and yield traits of barley under a water availability gradient. A case study comparing different spatial adjustments

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