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 Genome Biology , 2002, DOI: 10.1186/gb-2002-3-8-reviews1021 Abstract: Proteins are machines created by evolution, but it is unclear just how finely evolution has guided their sequence, structure, and function. It is undoubtedly true that individual mutations in a protein affect both its structure and its function and that such mutations can be fixed during evolutionary history, but it is also true that there are other elements of protein sequence that have been acted upon by evolution. For example, the genetic code appears to be laid out so that mutations and errors in translation are minimally damaging to protein structure and function [1]. Could the probability that a beneficial mutation is found and fixed in the population also have been manipulated during the course of evolution, so that the proteins we see today are more capable of change than the proteins that may have been cobbled together following the 'invention' of translation? Have proteins, in fact, evolved to evolve? There is already some evidence that bacteria are equipped to evolve phenotypes that are more capable of further adaptation (reviewed in [2,3,4]). For example, mutator [5] and hyper-recombinogenic [6] strains arise as a result of selection experiments. The development of DNA shuffling (reviewed in [7,8]) and the appearance of several recent papers using this technique [9,10,11] provide us with a surprising new opportunity to ask and answer these fundamental questions at the level of individual genes, and perhaps even genomes.DNA shuffling, a method for in vitro recombination, was developed as a technique to generate mutant genes that would encode proteins with improved or unique functionality [12,13]. It consists of a three-step process that begins with the enzymatic digestion of genes, yielding smaller fragments of DNA. The small fragments are then allowed to randomly hybridize and are filled in to create longer fragments. Ultimately, any full-length, recombined genes that are recreated are amplified via the polymerase chain reaction. If a series of alleles o
 Erik van Zwet Statistics , 2014, Abstract: In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the Bayes risk of the rule is {\em as if} the prior distribution of the parameter is partially exchangeable with respect to $G$. We provide a symmetrization technique for incorporating partial exchangeability of $\theta$ into a statistical model, without assuming any other prior information. We refer to this technique as {\em shuffling}. Shuffling can be viewed as an instance of empirical Bayes, where we estimate the (unordered) multiset of parameter values $\{\theta_1,\theta_2,\dots,\theta_p\}$ while using a uniform prior on $G$ for their ordering. Estimation of the multiset is a missing data problem which can be tackled with a stochastic EM algorithm. We show that in the special case of estimating the mean-value parameter in a regular exponential family model, shuffling leads to an estimator that is a weighted average of permuted versions of the usual maximum likelihood estimator. This is a novel form of shrinkage.