2,257 research outputs found
A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data
We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the
low signal-to-noise regime. This method builds on and complements the
previously described CMB Gibbs sampler, and effectively solves the low
signal-to-noise inefficiency problem of the direct Gibbs sampler. The new
algorithm is a simple Metropolis-Hastings sampler with a general proposal rule
for the power spectrum, C_l, followed by a particular deterministic rescaling
operation of the sky signal. The acceptance probability for this joint move
depends on the sky map only through the difference of chi-squared between the
original and proposed sky sample, which is close to unity in the low
signal-to-noise regime. The algorithm is completed by alternating this move
with a standard Gibbs move. Together, these two proposals constitute a
computationally efficient algorithm for mapping out the full joint CMB
posterior, both in the high and low signal-to-noise regimes.Comment: Submitted to Ap
Bayesian analysis of the low-resolution polarized 3-year WMAP sky maps
We apply a previously developed Gibbs sampling framework to the foreground
corrected 3-yr WMAP polarization data and compute the power spectrum and
residual foreground template amplitude posterior distributions. We first
analyze the co-added Q- and V-band data, and compare our results to the
likelihood code published by the WMAP team. We find good agreement, and thus
verify the numerics and data processing steps of both approaches. However, we
also analyze the Q- and V-bands separately, allowing for non-zero EB
cross-correlations and including two individual foreground template amplitudes
tracing synchrotron and dust emission. In these analyses, we find tentative
evidence of systematics: The foreground tracers correlate with each of the Q-
and V-band sky maps individually, although not with the co-added QV map; there
is a noticeable negative EB cross-correlation at l <~ 16 in the V-band map; and
finally, when relaxing the constraints on EB and BB, noticeable differences are
observed between the marginalized band powers in the Q- and V-bands. Further
studies of these features are imperative, given the importance of the low-l EE
spectrum on the optical depth of reionization tau and the spectral index of
scalar perturbations n_s.Comment: 5 pages, 4 figures, submitted to ApJ
Bayesian Power Spectrum Analysis of the First-Year WMAP data
We present the first results from a Bayesian analysis of the WMAP first year
data using a Gibbs sampling technique. Using two independent, parallel
supercomputer codes we analyze the WMAP Q, V and W bands. The analysis results
in a full probabilistic description of the information the WMAP data set
contains about the power spectrum and the all-sky map of the cosmic microwave
background anisotropies. We present the complete probability distributions for
each C_l including any non-Gaussianities of the power spectrum likelihood.
While we find good overall agreement with the previously published WMAP
spectrum, our analysis uncovers discrepancies in the power spectrum estimates
at low l multipoles. For example we claim the best-fit Lambda-CDM model is
consistent with the C_2 inferred from our combined Q+V+W analysis with a 10%
probability of an even larger theoretical C_2. Based on our exact analysis we
can therefore attribute the "low quadrupole issue" to a statistical
fluctuation.Comment: 5 pages. 4 figures. For additional information and data see
http://www.astro.uiuc.edu/~iodwyer/research#wma
Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton
The three Minkowski functionals and the recently defined length of the
skeleton are estimated for the co-added first-year Wilkinson Microwave
Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations,
based on Gaussian fluctuations with the a-priori best-fit running-index power
spectrum and WMAP-like beam and noise properties. Several power
spectrum-dependent quantities, such as the number of stationary points, the
total length of the skeleton, and a spectral parameter, gamma, are also
estimated. While the area and length Minkowski functionals and the length of
the skeleton show no evidence for departures from the Gaussian hypothesis, the
northern hemisphere genus has a chi^2 that is large at the 95% level for all
scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger
than that found in 99.5% of the simulations. In addition, the WMAP genus for
negative thresholds in the northern hemisphere has an amplitude that is larger
than in the simulations with a significance of more than 3 sigma. On the
smallest angular scales considered, the number of extrema in the WMAP data is
high at the 3 sigma level. However, this can probably be attributed to the
effect of point sources. Finally, the spectral parameter gamma is high at the
99% level in the northern Galactic hemisphere, while perfectly acceptable in
the southern hemisphere. The results provide strong evidence for the presence
of both non-Gaussian behavior and an unexpected power asymmetry between the
northern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap
Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation
We revisit the problem of exact CMB likelihood and power spectrum estimation
with the goal of minimizing computational cost through linear compression. This
idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and
here we develop it into a fully working computational framework for large-scale
polarization analysis, adopting \WMAP\ as a worked example. We compare five
different linear bases (pixel space, harmonic space, noise covariance
eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise
covariance eigenvectors) in terms of compression efficiency, and find that the
computationally most efficient basis is the signal-to-noise eigenvector basis,
which is closely related to the Karhunen-Loeve and Principal Component
transforms, in agreement with previous suggestions. For this basis, the
information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a
smaller set of 3102 modes, with a maximum error increase of any single
multipole of 3.8\% at , and a maximum shift in the mean values of a
joint distribution of an amplitude--tilt model of 0.006. This
compression reduces the computational cost of a single likelihood evaluation by
a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust
likelihood by implicitly regularizing nearly degenerate modes. Finally, we use
the same compression framework to formulate a numerically stable and
computationally efficient variation of the Quadratic Maximum Likelihood
implementation that requires less than 3 GB of memory and 2 CPU minutes per
iteration for , rendering low- QML CMB power spectrum
analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ
Modernisation of the Norwegian Tide Gauge Network
The modernization of the Norwegian Tide Gauge Network using technologies of the 1980s is presented. Technical and organizational challenges are described in detail together with cost-estimates and possible future developments
Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation
Einstein's relation E=Mc^2 between the energy E and the mass M is the
cornerstone of the relativity theory. This relation is often derived in a
context of the relativistic theory for closed systems which do not accelerate.
By contrast, Newtonian approach to the mass is based on an accelerated motion.
We study here a particular neoclassical field model of a particle governed by a
nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the
nonlinear KG equation and its energy density concentrate at a trajectory, then
this trajectory and the energy must satisfy the relativistic version of
Newton's law with the mass satisfying Einstein's relation. Therefore the
internal energy of a localized wave affects its acceleration in an external
field as the inertial mass does in Newtonian mechanics. We demonstrate that the
"concentration" assumptions hold for a wide class of rectilinear accelerating
motions
A re-analysis of the three-year WMAP temperature power spectrum and likelihood
We analyze the three-year WMAP temperature anisotropy data seeking to confirm
the power spectrum and likelihoods published by the WMAP team. We apply five
independent implementations of four algorithms to the power spectrum estimation
and two implementations to the parameter estimation. Our single most important
result is that we broadly confirm the WMAP power spectrum and analysis. Still,
we do find two small but potentially important discrepancies: On large angular
scales there is a small power excess in the WMAP spectrum (5-10% at l<~30)
primarily due to likelihood approximation issues between 13 <= l <~30. On small
angular scales there is a systematic difference between the V- and W-band
spectra (few percent at l>~300). Recently, the latter discrepancy was explained
by Huffenberger et al. (2006) in terms of over-subtraction of unresolved point
sources. As far as the low-l bias is concerned, most parameters are affected by
a few tenths of a sigma. The most important effect is seen in n_s. For the
combination of WMAP, Acbar and BOOMERanG, the significance of n_s =/ 1 drops
from ~2.7 sigma to ~2.3 sigma when correcting for this bias. We propose a few
simple improvements to the low-l WMAP likelihood code, and introduce two
important extensions to the Gibbs sampling method that allows for proper
sampling of the low signal-to-noise regime. Finally, we make the products from
the Gibbs sampling analysis publically available, thereby providing a fast and
simple route to the exact likelihood without the need of expensive matrix
inversions.Comment: 14 pages, 7 figures. Accepted for publication in ApJ. Numerical
results unchanged, but interpretation sharpened: Likelihood approximation
issues at l=13-30 far more important than potential foreground issues at l <=
12. Gibbs products (spectrum and sky samples, and "easy-to-use" likelihood
module) available from http://www.astro.uio.no/~hke/ under "Research
Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble
Eigenvalue correlations of random matrix ensembles as a function of an
external perturbation are investigated vis the Dyson Brownian Motion Model in
the situation where the level density has a hard edge singularity. By solving a
linearized hydrodynamical equation, a universal dependence of the
density-density correlator on the external field is found. As an application we
obtain a formula for the variance of linear statistics with the parametric
dependence exhibited as a Laplace transform.Comment: 23 pages, late
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