89 research outputs found
Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks
This paper considers the nonparametric maximum likelihood estimator (MLE) for
the joint distribution function of an interval censored survival time and a
continuous mark variable. We provide a new explicit formula for the MLE in this
problem. We use this formula and the mark specific cumulative hazard function
of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This
result leads to necessary and sufficient conditions for consistency of the MLE
which imply that the MLE is inconsistent in general. We show that the
inconsistency can be repaired by discretizing the marks. Our theoretical
results are supported by simulations.Comment: 27 pages, 4 figure
The effect of asymmetric beams in the Wilkinson Microwave Anisotropy Probe experiment
We generate simulations of the CMB temperature field as observed by the WMAP
satellite, taking into account the detailed shape of the asymmetric beams and
scanning strategy of the experiment, and use these to re-estimate the WMAP beam
transfer functions. This method avoids the need of artificially symmetrizing
the beams, as done in the baseline WMAP approach, and instead measures the
total convolution effect by direct simulation. We find only small differences
with respect to the nominal transfer functions, typically less than 1%
everywhere, and less than 0.5% at l<400. The net effect on the CMB power
spectrum is less than 0.6%. The effect on all considered cosmological
parameters are negligible. For instance, we find that the spectral index of
scalar perturbations after taking into account the beam asymmetries is n_s =
0.964 +- 0.014, corresponding to a negative shift of -0.1 sigma compared to the
previously released WMAP results. Our CMB sky simulations are made publicly
available, and can be used for general studies of asymmetric beam effects in
the WMAP data.Comment: 14 pages, 7 figures, published versio
The Effect of Asymmetric Beams in the Wilkinson Microwave Anisotropy Probe Experiment
We generate simulations of the cosmic microwave background (CMB) temperature field as observed by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, taking into account the detailed shape of the asymmetric beams and scanning strategy of the experiment, and use these to re-estimate the WMAP beam transfer functions. This method avoids the need of artificially symmetrizing the beams, as done in the baseline WMAP approach, and instead measures the total convolution effect by direct simulation. We find only small differences with respect to the nominal transfer functions, typically less than 1% everywhere, and less than 0.5% at ℓ < 400. The net effect on the CMB power spectrum is less than 0.6%. The effect on all considered cosmological parameters is negligible. For instance, we find that the spectral index of scalar perturbations after taking into account the beam asymmetries is n_s = 0.964 ± 0.014, corresponding to a negative shift of –0.1σ compared to the previously released WMAP results. Our CMB sky simulations are made publicly available and can be used for general studies of asymmetric beam effects in the WMAP data
CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator
We introduce a new CMB temperature likelihood approximation called the
Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by
transforming the observed marginal power spectrum distributions obtained by the
CMB Gibbs sampler into standard univariate Gaussians, and then approximate
their joint transformed distribution by a multivariate Gaussian. The method is
exact for full-sky coverage and uniform noise, and an excellent approximation
for sky cuts and scanning patterns relevant for modern satellite experiments
such as WMAP and Planck. A single evaluation of this estimator between l=2 and
200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space
likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires
~20 seconds. We apply this tool to the 5-year WMAP temperature data, and
re-estimate the angular temperature power spectrum, , and likelihood,
L(C_l), for l<=200, and derive new cosmological parameters for the standard
six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the
official WMAP spectrum, but we find slight differences in the derived
cosmological parameters. Most importantly, the spectral index of scalar
perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma
higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that
an exact likelihood treatment is required to higher l's than previously
believed, reinforcing and extending our conclusions from the 3-year WMAP
analysis. In that case, we found that the sub-optimal likelihood approximation
adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while
here we find that the same approximation between l=30 and 200 introduces a bias
of 0.6 sigma in n_s.Comment: 10 pages, 7 figures, submitted to Ap
Frequentist comparison of CMB local extrema statistics in the five-year WMAP data with two anisotropic cosmological models
We present local extrema studies of two models that introduce a preferred
direction into the observed cosmic microwave background (CMB) temperature
field. In particular, we make a frequentist comparison of the one- and
two-point statistics for the dipole modulation and ACW models with data from
the five-year Wilkinson Microwave Anisotropy Probe (WMAP). This analysis is
motivated by previously revealed anomalies in the WMAP data, and particularly
the difference in the statistical nature of the temperature anisotropies when
analysed in hemispherical partitions.
The analysis of the one-point statistics indicates that the previously
determined hemispherical variance difficulties can be apparently overcome by a
dipole modulation field, but new inconsistencies arise if the mean and the
l-dependence of the statistics are considered. The two-point correlation
functions of the local extrema, the temperature pair product and the
point-point spatial pair-count, demonstrate that the impact of such a
modulation is to over-`asymmetrise' the temperature field on smaller scales
than the wave-length of the dipole or quadrupole, and this is disfavored by the
observed data.The results from the ACW model predictions, however, are
consistent with the standard isotropic hypothesis. The two-point analysis
confirms that the impact of this type of violation of isotropy on the
temperature extrema statistics is relatively weak.
From this work, we conclude that a model with more spatial structure than the
dipole modulated or rotational-invariance breaking models are required to fully
explain the observed large-scale anomalies in the WMAP data.Comment: 10 pages, 4 figures, 3 tables, accepted for publication in MNRA
Non-detection of a statistically anisotropic power spectrum in large-scale structure
We search a sample of photometric luminous red galaxies (LRGs) measured by
the Sloan Digital Sky Survey (SDSS) for a quadrupolar anisotropy in the
primordial power spectrum, in which P(\vec{k}) is an isotropic power spectrum
P(k) multiplied by a quadrupolar modulation pattern. We first place limits on
the 5 coefficients of a general quadrupole anisotropy. We also consider
axisymmetric quadrupoles of the form P(\vec{k}) = P(k){1 +
g_*[(\hat{k}\cdot\hat{n})^2-1/3]} where \hat{n} is the axis of the anisotropy.
When we force the symmetry axis \hat{n} to be in the direction (l,b)=(94
degrees,26 degrees) identified in the recent Groeneboom et al. analysis of the
cosmic microwave background, we find g_*=0.006+/-0.036 (1 sigma). With uniform
priors on \hat{n} and g_* we find that -0.41<g_*<+0.38 with 95% probability,
with the wide range due mainly to the large uncertainty of asymmetries aligned
with the Galactic Plane. In none of these three analyses do we detect evidence
for quadrupolar power anisotropy in large scale structure.Comment: 23 pages; 10 figures; 3 tables; replaced with version published in
JCAP (added discussion of scale-varying quadrupolar anisotropy
Anisotropic Inflation with Non-Abelian Gauge Kinetic Function
We study an anisotropic inflation model with a gauge kinetic function for a
non-abelian gauge field. We find that, in contrast to abelian models, the
anisotropy can be either a prolate or an oblate type, which could lead to a
different prediction from abelian models for the statistical anisotropy in the
power spectrum of cosmological fluctuations. During a reheating phase, we find
chaotic behaviour of the non-abelian gauge field which is caused by the
nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of
the chaos which turns out to be uncorrelated with the anisotropy.Comment: 16 pages, 4 figure
Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies?
(Abridged) A simple six-parameter LCDM model provides a successful fit to
WMAP data, both when the data are analyzed alone and in combination with other
cosmological data. Even so, it is appropriate to search for any hints of
deviations from the now standard model of cosmology, which includes inflation,
dark energy, dark matter, baryons, and neutrinos. The cosmological community
has subjected the WMAP data to extensive and varied analyses. While there is
widespread agreement as to the overall success of the six-parameter LCDM model,
various "anomalies" have been reported relative to that model. In this paper we
examine potential anomalies and present analyses and assessments of their
significance. In most cases we find that claimed anomalies depend on posterior
selection of some aspect or subset of the data. Compared with sky simulations
based on the best fit model, one can select for low probability features of the
WMAP data. Low probability features are expected, but it is not usually
straightforward to determine whether any particular low probability feature is
the result of the a posteriori selection or of non-standard cosmology. We
examine in detail the properties of the power spectrum with respect to the LCDM
model. We examine several potential or previously claimed anomalies in the sky
maps and power spectra, including cold spots, low quadrupole power,
quadropole-octupole alignment, hemispherical or dipole power asymmetry, and
quadrupole power asymmetry. We conclude that there is no compelling evidence
for deviations from the LCDM model, which is generally an acceptable
statistical fit to WMAP and other cosmological data.Comment: 19 pages, 17 figures, also available with higher-res figures on
http://lambda.gsfc.nasa.gov; accepted by ApJS; (v2) text as accepte
- …