The stochastic order of probability measures on ordered metric spaces

The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of probability measures on ordered Banach spaces, we introduce and study a stochastic order on the space of probability measures $\mathcal{P}(X)$, where $X$ is a metric space equipped with a closed partial order, and derive several useful equivalent versions of the definition. We establish the antisymmetry and closedness of the stochastic order (and hence that it is a closed partial order) for the case of a partial order on a Banach space induced by a closed normal cone with interior. We also consider order-completeness of the stochastic order for a cone of a finite-dimensional Banach space and derive a version of the arithmetic-geometric-harmonic mean inequalities in the setting of the associated probability space on positive matrices.Comment: 25 page

Additional file 6 of LinkImputeR: user-guided genotype calling and imputation for non-model organisms

Full cannabis results. (DOCX 13 kb

Additional file 3: Figure S1. of Genomic ancestry estimation quantifies use of wild species in grape breeding

Distance (kb) between filtered SNPs used for ancestry estimation. (PDF 96 kb

Additional file 1: Table S1. of Genomic ancestry estimation quantifies use of wild species in grape breeding

A list of the 78 cultivars used in this study as well as location and institute. Sample information is also provided for the additional 16 samples which were discarded during the genotyping analysis pipeline and they are highlighted in yellow. (XLSX 27 kb

Additional file 2: Table S2. of Genomic ancestry estimation quantifies use of wild species in grape breeding

Matrix of genome-wide average IBS values for 64 hybrids. (XLSX 82 kb