31,632 research outputs found
Bridge Simulation and Metric Estimation on Landmark Manifolds
We present an inference algorithm and connected Monte Carlo based estimation
procedures for metric estimation from landmark configurations distributed
according to the transition distribution of a Riemannian Brownian motion
arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric.
The distribution possesses properties similar to the regular Euclidean normal
distribution but its transition density is governed by a high-dimensional PDE
with no closed-form solution in the nonlinear case. We show how the density can
be numerically approximated by Monte Carlo sampling of conditioned Brownian
bridges, and we use this to estimate parameters of the LDDMM kernel and thus
the metric structure by maximum likelihood
Testing physical models for dipolar asymmetry with CMB polarization
The cosmic microwave background (CMB) temperature anisotropies exhibit a
large-scale dipolar power asymmetry. To determine whether this is due to a
real, physical modulation or is simply a large statistical fluctuation requires
the measurement of new modes. Here we forecast how well CMB polarization data
from \Planck\ and future experiments will be able to confirm or constrain
physical models for modulation. Fitting several such models to the \Planck\
temperature data allows us to provide predictions for polarization asymmetry.
While for some models and parameters \Planck\ polarization will decrease error
bars on the modulation amplitude by only a small percentage, we show,
importantly, that cosmic-variance-limited (and in some cases even \Planck)
polarization data can decrease the errors by considerably better than the
expectation of based on simple -space arguments. We project
that if the primordial fluctuations are truly modulated (with parameters as
indicated by \Planck\ temperature data) then \Planck\ will be able to make a
2 detection of the modulation model with 20--75\% probability,
increasing to 45--99\% when cosmic-variance-limited polarization is considered.
We stress that these results are quite model dependent. Cosmic variance in
temperature is important: combining statistically isotropic polarization with
temperature data will spuriously increase the significance of the temperature
signal with 30\% probability for \Planck.Comment: 18 pages, 11 figures, 2 tables. Version updated to match PRD versio
Bayesian inference on the sphere beyond statistical isotropy
We present a general method for Bayesian inference of the underlying
covariance structure of random fields on a sphere. We employ the Bipolar
Spherical Harmonic (BipoSH) representation of general covariance structure on
the sphere. We illustrate the efficacy of the method as a principled approach
to assess violation of statistical isotropy (SI) in the sky maps of Cosmic
Microwave Background (CMB) fluctuations. SI violation in observed CMB maps
arise due to known physical effects such as Doppler boost and weak lensing; yet
unknown theoretical possibilities like cosmic topology and subtle violations of
the cosmological principle, as well as, expected observational artefacts of
scanning the sky with a non-circular beam, masking, foreground residuals,
anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI
violation signals with their full statistics in simulated CMB maps. Our
formalism easily adapts to exploring parametric physical models with non-SI
covariance, as we illustrate for the inference of the parameters of a Doppler
boosted sky map. Our approach promises to provide a robust quantitative
evaluation of the evidence for SI violation related anomalies in the CMB sky by
estimating the BipoSH spectra along with their complete posterior.Comment: 16 pages, 6 figure
Hierarchical Cosmic Shear Power Spectrum Inference
We develop a Bayesian hierarchical modelling approach for cosmic shear power
spectrum inference, jointly sampling from the posterior distribution of the
cosmic shear field and its (tomographic) power spectra. Inference of the shear
power spectrum is a powerful intermediate product for a cosmic shear analysis,
since it requires very few model assumptions and can be used to perform
inference on a wide range of cosmological models \emph{a posteriori} without
loss of information. We show that joint posterior for the shear map and power
spectrum can be sampled effectively by Gibbs sampling, iteratively drawing
samples from the map and power spectrum, each conditional on the other. This
approach neatly circumvents difficulties associated with complicated survey
geometry and masks that plague frequentist power spectrum estimators, since the
power spectrum inference provides prior information about the field in masked
regions at every sampling step. We demonstrate this approach for inference of
tomographic shear -mode, -mode and -cross power spectra from a
simulated galaxy shear catalogue with a number of important features; galaxies
distributed on the sky and in redshift with photometric redshift uncertainties,
realistic random ellipticity noise for every galaxy and a complicated survey
mask. The obtained posterior distributions for the tomographic power spectrum
coefficients recover the underlying simulated power spectra for both - and
-modes.Comment: 16 pages, 8 figures, accepted by MNRA
Image Sampling with Quasicrystals
We investigate the use of quasicrystals in image sampling. Quasicrystals
produce space-filling, non-periodic point sets that are uniformly discrete and
relatively dense, thereby ensuring the sample sites are evenly spread out
throughout the sampled image. Their self-similar structure can be attractive
for creating sampling patterns endowed with a decorative symmetry. We present a
brief general overview of the algebraic theory of cut-and-project quasicrystals
based on the geometry of the golden ratio. To assess the practical utility of
quasicrystal sampling, we evaluate the visual effects of a variety of
non-adaptive image sampling strategies on photorealistic image reconstruction
and non-photorealistic image rendering used in multiresolution image
representations. For computer visualization of point sets used in image
sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary
materials, please visit at
http://www.Eyemaginary.com/Portfolio/Publications.htm
On the Statistical Significance of the Bulk Flow Measured by the PLANCK Satellite
A recent analysis of data collected by the Planck satellite detected a net
dipole at the location of X-ray selected galaxy clusters, corresponding to a
large-scale bulk flow extending at least to , the median redshift
of the cluster sample. The amplitude of this flow, as measured with Planck, is
consistent with earlier findings based on data from the Wilkinson Microwave
Anisotropy Probe (WMAP). However, the uncertainty assigned to the dipole by the
Planck team is much larger than that found in the WMAP studies, leading the
authors of the Planck study to conclude that the observed bulk flow is not
statistically significant. We here show that two of the three implementations
of random sampling used in the error analysis of the Planck study lead to
systematic overestimates in the uncertainty of the measured dipole. Random
simulations of the sky do not take into account that the actual realization of
the sky leads to filtered data that have a 12% lower root-mean-square
dispersion than the average simulation. Using rotations around the Galactic
pole (the Z axis), increases the uncertainty of the X and Y components of the
dipole and artificially reduces the significance of the dipole detection from
98-99% to less than 90% confidence. When either effect is taken into account,
the corrected errors agree with those obtained using random distributions of
clusters on Planck data, and the resulting statistical significance of the
dipole measured by Planck is consistent with that of the WMAP results.Comment: A & A, in pres
Sparse Inpainting and Isotropy
Sparse inpainting techniques are gaining in popularity as a tool for
cosmological data analysis, in particular for handling data which present
masked regions and missing observations. We investigate here the relationship
between sparse inpainting techniques using the spherical harmonic basis as a
dictionary and the isotropy properties of cosmological maps, as for instance
those arising from cosmic microwave background (CMB) experiments. In
particular, we investigate the possibility that inpainted maps may exhibit
anisotropies in the behaviour of higher-order angular polyspectra. We provide
analytic computations and simulations of inpainted maps for a Gaussian
isotropic model of CMB data, suggesting that the resulting angular trispectrum
may exhibit small but non-negligible deviations from isotropy.Comment: 18 pages, 6 figures. v3: matches version published in JCAP;
formatting changes and single typo correction only. Code available from
http://zuserver2.star.ucl.ac.uk/~smf/code.htm
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