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Total Positivity in Markov Structures
(Institute of Mathematical StatisticsAnnals of Statistics, 2017-06)
We discuss properties of distributions that are multivariate totally positive of order two (MTP$_{2}$) related to conditional independence. In particular, we show that any independence model generated by an MTP$_{2}$ ...
Pairwise Markov properties for regression graphs
(WileyStat, 2016-11-13)
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ...
Bayesian Nonparametric Ordination for the Analysis of Microbial Communities
(Taylor & FrancisJournal of the American Statistical Association, 2017-07-10)
Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency ...
Trend to equilibrium for the Becker–Döring equations: an analogue of Cercignani's conjecture
(Mathematical Sciences PublishersAnalysis and PDE, 2017-08-01)
We investigate the rate of convergence to equilibrium for subcritical solutions to the Becker–Döring equations with physically relevant coagulation and fragmentation coefficients and mild assumptions on the given initial ...
Homological mirror symmetry for hypersurface cusp singularities
(SpringerSelecta Mathematica, 2017-06-03)
We study versions of homological mirror symmetry for hypersurface cusp singularities and the three hypersurface simple elliptic singularities. We show that the Milnor fibres of each of these carries a distinguished Lefschetz ...
Trust in numbers
(WileyJournal of the Royal Statistical Society. Series A: Statistics in Society, 2017-10-01)
Those who value quantitative and scientific evidence are faced with claims both of a reproducibility crisis in scientific publication, and of a post-truth society abounding in fake news and alternative facts. Both issues ...
D-modules on rigid analytic spaces II: Kashiwara’s equivalence
(American Mathematical SocietyJournal of Algebraic Geometry, 2018-01-01)
Let X be a smooth rigid analytic space. We prove that the category of co-admissible D-cap-modules on a smooth rigid analytic space supported on a closed smooth subvariety is naturally equivalent to the category of co-admissible ...
Discussion of "The ASA’s p-value statement, one year on" by Robert Matthews
(Wiley-BlackwellSignificance, 2017-05-03)
Graphical representations of Ising and Potts models: stochastic geometry of the quantum Ising model and the space-time Potts model
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsStatistical LaboratoryGonville & Caius College, 2010-02-09)
Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic
properties as ...
On eigenvectors for semisimple elements in actions of algebraic groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-02-09)
Let $G$ be a simple simply connected algebraic group defined over an algebraically closed field $K$ and $V$ an irreducible module defined over $K$ on which $G$ acts. Let $E$ denote the set of vectors in $V$ which are ...