Statistical analysis on high-dimensional spheres and shape spaces

We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines. First the uniform measure on the infinite-dimensional sphere is reviewed, together with connections with Wiener measure. We then discuss densities of Gaussian measures with respect to Wiener measure. Some nonuniform distributions on infinite-dimensional spheres and shape spaces are introduced, and special cases which have important practical consequences are considered. We focus on the high-dimensional real and complex Bingham, uniform, von Mises-Fisher, Fisher-Bingham and the real and complex Watson distributions. Asymptotic distributions in the cases where dimension and sample size are large are discussed. Approximations for practical maximum likelihood based inference are considered, and in particular we discuss an application to brain shape modeling.Comment: Published at http://dx.doi.org/10.1214/009053605000000264 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The oxygen isotopic composition of water extracted from carbonaceous chondrites

The oxygen isotopic composition of water from carbonaceous chondrites suggests that close to isotopic equilibrium was attained on CI and CM parent bodies. This is more consistent with a closed system than one with fluid flow. Tagish Lake does not display such equilibrium

Bayesian matching of unlabelled point sets using Procrustes and configuration models

The problem of matching unlabelled point sets using Bayesian inference is considered. Two recently proposed models for the likelihood are compared, based on the Procrustes size-and-shape and the full configuration. Bayesian inference is carried out for matching point sets using Markov chain Monte Carlo simulation. An improvement to the existing Procrustes algorithm is proposed which improves convergence rates, using occasional large jumps in the burn-in period. The Procrustes and configuration methods are compared in a simulation study and using real data, where it is of interest to estimate the strengths of matches between protein binding sites. The performance of both methods is generally quite similar, and a connection between the two models is made using a Laplace approximation

An analysis of HCN observations of the Circumnuclear Disk at the galactic centre

The Circumnuclear Disk (CND) is a torus of dust and molecular gas rotating about the galactic centre and extending from approximately 1.6pc to 7pc from the central massive black hole, SgrA*. Large Velocity Gradient modelling of the intensities of the HCN 1-0, 3-2 and 4-3 transitions is used to infer hydrogen density and HCN optical depth. From HCN observations we find the molecular hydrogen density ranges from 0.1 to 2 $\times$ 10$^{6}$ cm$^{-3}$, about an order of magnitude less than inferred previously. The 1-0 line is weakly inverted with line-centre optical depth approx $-$0.1, in stark contrast to earlier estimates of 4. The estimated mass of the ring is approximately 3 $-$ 4 $\times$ 10$^{5}$M$_{\odot}$ consistent with estimates based on thermal dust emission. The tidal shear in the disk implies that star formation is not expected to occur without some significant triggering event.Comment: 17 pages, 8 figures, 7 tables (including 3 landscape tables generated with 2 separate Latex files

SKA Engineering Change Proposal: Gridded Visibilities to Enable Precision Cosmology with Radio Weak Lensing

This document was submitted as supporting material to an Engineering Change Proposal (ECP) for the Square Kilometre Array (SKA). This ECP requests gridded visibilities as an extra imaging data product from the SKA, in order to enable bespoke analysis techniques to measure source morphologies to the accuracy necessary for precision cosmology with radio weak lensing. We also discuss the properties of an SKA weak lensing data set and potential overlaps with other cosmology science goals.Comment: Comments welcome. 4 pages, 3 figures. Progress can be tracked at the SKA ECP register https://skaoffice.atlassian.net/wiki/display/EP/ECP+Registe

New data on carbon isotopic compositions of some ureilites

We have collected new C data from high resolution stepped combustion analyses of 5 ureilites to better constrain their relationships with O and mineralogical/petrographic groupings. This may help the future development of petrogenetic models