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Notably, they extend to general designs the risk reduction achieved by Stein's multiple shrinkage estimators for balanced observations on an array of means.
Our results (not shown here) indicated that there is no advantage in specifying multiple shrinkage targets.
To further investigate the usefulness of multiple shrinkage targets, we partitioned the genes into 10 groups according to the ranges of and applied the shrinkage separately to each group.
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Instead, the number of pigeons had fluctuated by up to 1000-fold during multiple population shrinkages and growths over the previous million years.
That approach was extended by Durrant and Mott (2010), who describe a partially Bayesian mixed model of QTL mapping: By focusing on additive effects of QTL for normally distributed traits with no additional covariates or population structure, they provided an efficient method for combined multiple imputation and shrinkage estimation via complete factorization of a pseudo-posterior.
For a low number of pilots, improved results are possible using multiple frames or biased shrinkage estimates [27].
For example, we have previously shown that the neurotoxicity of platinum-based drugs correlates with the rate of dorsal root ganglion nucleolus shrinkage during multiple-dose drug treatment (McKeage et al, 2001).
The major difficulties in implementing this idea are the development of an efficient algorithm to detect all undesirable patterns of different scales and the hierarchical application of the wavelet shrinkage method over multiple scales.
For the data application, the Gelman and Rubin's diagnostic on multiple MCMC chains produced a shrinkage factor < 1.2 (Colosimo and Del Castillo 2007).
In contrast, Silva et al. [ 25] who focused on blocks of conserved synteny, found that genome shrinkage arose through multiple events of gene disintegration dispersed over the whole genome, which would be better explained by selection acting on individual genes even in these early steps.
Van de Wiel et al. [ 36] proposed ShrinkHT, a Bayesian method for shrinking multiple parameters in a statistical model where 'shrinkage' refers to borrowing information across features.
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