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环境序列样本的系统发育 Kantorovich–Rubinstein 距离AI 解读

Summary It is now common to survey microbial communities by sequencing nucleic acid material extracted in bulk from a given environment. Comparative methods are needed that indicate the extent to which two communities differ given data sets of this type. UniFrac, which gives a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses. We provide a foundation for such methods by establishing that, if we…

收缩估计量、Skorokhod 问题与随机分部积分AI 解读

For a broad class of error distributions that includes the spherically symmetric ones, we give a short proof that the usual estimator of the mean in a d-dimensional shift model is inadmissible under quadratic loss when $d \geq 3$. Our proof involves representing the error distribution as that of a stopped Brownian motion and using elementary stochastic analysis to obtain a generalization of an integration by parts lemma due to Stein in the Gaussian case.

系统发育推断中若干概率模型的不变量AI 解读

The so-called method of invariants is a technique in the field of molecular evolution for inferring phylogenetic relations among a number of species on the basis of nucleotide sequence data. An invariant is a polynomial function of the probability distribution defined by a stochastic model for the observed nucleotide sequence. This function has the special property that it is identically zero for one possible phylogeny and typically nonzero for another possible phylogeny.…