Analysis of multivariate data sets from, for example, microarray studies frequently results in lists of genes which are associated with some response of interest. The biological interpretation is often complicated by the statistical instability of the obtained gene lists, which may partly be due to the functional redundancy among genes, implying that multiple genes can play exchangeable roles i...

A black substance exuding from fractures was observed in 2012 Ytterby mine, Sweden, and identified 2017 as birnessite with the composition Mx[Mn(III,IV)]2O4∙(H2O)n. M is usually calcium sodium, x around 0.5. The unique, being calcium, magnesium, also rare earth elements (REEs) constituting up to 2% of total metal content. biogenic origin established 2018. Analysis microbial processes leading fo...

In this note, we provide an elementary analysis of the prediction error ridge regression with random design. The proof is short and self-contained. particular, it bypasses use Rudelson’s deviation inequality for covariance matrices, through a combination exchangeability arguments, matrix perturbation operator convexity.

This work proposes a new exchangeability test for random sequence through martingale-based approach. Its main contributions include 1) an additive martingale which is more amenable designing tests by exploiting the Hoeffding-Azuma lemma and 2) different betting functions constructing martingale. By choosing underlying probability density function of p-values as function, it can be shown that, w...