5,176 research outputs found
Constraining Isocurvature Initial Conditions with WMAP 3-year data
We present constraints on the presence of isocurvature modes from the
temperature and polarization CMB spectrum data from the WMAP satellite alone,
and in combination with other datasets including SDSS galaxy survey and SNLS
supernovae. We find that the inclusion of polarization data allows the WMAP
data alone, as well as in combination with complementary observations, to place
improved limits on the contribution of CDM and neutrino density isocurvature
components individually. With general correlations, the upper limits on these
sub-dominant isocurvature components are reduced to ~60% of the first year WMAP
results, with specific limits depending on the type of fluctuations. If
multiple isocurvature components are allowed, however, we find that the data
still allow a majority of the initial power to come from isocurvature modes. As
well as providing general constraints we also consider their interpretation in
light of specific theoretical models like the curvaton and double inflation.Comment: 8 pages, 7 figures. Revised Sec 4 and Figs 3-4 post-publication to
correct an error for models with varying isocurvature spectral inde
THERMAL RADIATION FROM MAGNETIZED NEUTRON STARS: A look at the Surface of a Neutron Star.
Surface thermal emission has been detected by ROSAT from four nearby young
neutron stars. Assuming black body emission, the significant pulsations of the
observed light curves can be interpreted as due to large surface temperature
differences produced by the effect of the crustal magnetic field on the flow of
heat from the hot interior toward the cooler surface. However, the energy
dependence of the modulation observed in Geminga is incompatible with blackbody
emission: this effect will give us a strong constraint on models of the neutron
star surface.Comment: 10 pages. tar-compressed and uuencoded postcript file. talk given at
the `Jubilee Gamow Seminar', St. Petersburg, Sept. 1994
Harold Jeffreys's Theory of Probability Revisited
Published exactly seventy years ago, Jeffreys's Theory of Probability (1939)
has had a unique impact on the Bayesian community and is now considered to be
one of the main classics in Bayesian Statistics as well as the initiator of the
objective Bayes school. In particular, its advances on the derivation of
noninformative priors as well as on the scaling of Bayes factors have had a
lasting impact on the field. However, the book reflects the characteristics of
the time, especially in terms of mathematical rigor. In this paper we point out
the fundamental aspects of this reference work, especially the thorough
coverage of testing problems and the construction of both estimation and
testing noninformative priors based on functional divergences. Our major aim
here is to help modern readers in navigating in this difficult text and in
concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968],
[arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073].
Rejoinder in [arXiv:0909.1008]. Published in at
http://dx.doi.org/10.1214/09-STS284 the Statistical Science
(http://www.imstat.org/sts/) by the Institute of Mathematical Statistics
(http://www.imstat.org
A Bayesian approach to the follow-up of candidate gravitational wave signals
Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo
and Tama-300) have now reached high sensitivity and duty cycle. We present a
Bayesian evidence-based approach to the search for gravitational waves, in
particular aimed at the followup of candidate events generated by the analysis
pipeline. We introduce and demonstrate an efficient method to compute the
evidence and odds ratio between different models, and illustrate this approach
using the specific case of the gravitational wave signal generated during the
inspiral phase of binary systems, modelled at the leading quadrupole Newtonian
order, in synthetic noise. We show that the method is effective in detecting
signals at the detection threshold and it is robust against (some types of)
instrumental artefacts. The computational efficiency of this method makes it
scalable to the analysis of all the triggers generated by the analysis
pipelines to search for coalescing binaries in surveys with ground-based
interferometers, and to a whole variety of signal waveforms, characterised by a
larger number of parameters.Comment: 9 page
A TV-Gaussian prior for infinite-dimensional Bayesian inverse problems and its numerical implementations
Many scientific and engineering problems require to perform Bayesian
inferences in function spaces, in which the unknowns are of infinite dimension.
In such problems, choosing an appropriate prior distribution is an important
task. In particular we consider problems where the function to infer is subject
to sharp jumps which render the commonly used Gaussian measures unsuitable. On
the other hand, the so-called total variation (TV) prior can only be defined in
a finite dimensional setting, and does not lead to a well-defined posterior
measure in function spaces. In this work we present a TV-Gaussian (TG) prior to
address such problems, where the TV term is used to detect sharp jumps of the
function, and the Gaussian distribution is used as a reference measure so that
it results in a well-defined posterior measure in the function space. We also
present an efficient Markov Chain Monte Carlo (MCMC) algorithm to draw samples
from the posterior distribution of the TG prior. With numerical examples we
demonstrate the performance of the TG prior and the efficiency of the proposed
MCMC algorithm
Model-based estimates of the finite population mean for two-stage cluster samples with unit non-response
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74917/1/j.1467-9876.2007.00566.x.pd
Bayesian coherent analysis of in-spiral gravitational wave signals with a detector network
The present operation of the ground-based network of gravitational-wave laser
interferometers in "enhanced" configuration brings the search for gravitational
waves into a regime where detection is highly plausible. The development of
techniques that allow us to discriminate a signal of astrophysical origin from
instrumental artefacts in the interferometer data and to extract the full range
of information are some of the primary goals of the current work. Here we
report the details of a Bayesian approach to the problem of inference for
gravitational wave observations using a network of instruments, for the
computation of the Bayes factor between two hypotheses and the evaluation of
the marginalised posterior density functions of the unknown model parameters.
The numerical algorithm to tackle the notoriously difficult problem of the
evaluation of large multi-dimensional integrals is based on a technique known
as Nested Sampling, which provides an attractive alternative to more
traditional Markov-chain Monte Carlo (MCMC) methods. We discuss the details of
the implementation of this algorithm and its performance against a Gaussian
model of the background noise, considering the specific case of the signal
produced by the in-spiral of binary systems of black holes and/or neutron
stars, although the method is completely general and can be applied to other
classes of sources. We also demonstrate the utility of this approach by
introducing a new coherence test to distinguish between the presence of a
coherent signal of astrophysical origin in the data of multiple instruments and
the presence of incoherent accidental artefacts, and the effects on the
estimation of the source parameters as a function of the number of instruments
in the network.Comment: 22 page
Habitat‐dependent occupancy and movement in a migrant songbird highlights the importance of mangroves and forested lagoons in Panama and Colombia
Climate change is predicted to impact tropical mangrove forests due to decreased rainfall, sea‐level rise, and increased seasonality of flooding. Such changes are likely to influence habitat quality for migratory songbirds occupying mangrove wetlands during the tropical dry season. Overwintering habitat quality is known to be associated with fitness in migratory songbirds, yet studies have focused primarily on territorial species. Little is known about the ecology of nonterritorial species that may display more complex movement patterns within and among habitats of differing quality. In this study, we assess within‐season survival and movement at two spatio‐temporal scales of a nonterritorial overwintering bird, the prothonotary warbler (Protonotaria citrea), that depends on mangroves and tropical lowland forests. Specifically, we (a) estimated within‐patch survival and persistence over a six‐week period using radio‐tagged birds in central Panama and (b) modeled abundance and occupancy dynamics at survey points throughout eastern Panama and northern Colombia as the dry season progressed. We found that site persistence was highest in mangroves; however, the probability of survival did not differ among habitats. The probability of warbler occupancy increased with canopy cover, and wet habitats were least likely to experience local extinction as the dry season progressed. We also found that warbler abundance is highest in forests with the tallest canopies. This study is one of the first to demonstrate habitat‐dependent occupancy and movement in a nonterritorial overwintering migrant songbird, and our findings highlight the need to conserve intact, mature mangrove, and lowland forests
Moving Beyond Noninformative Priors: Why and How to Choose Weakly Informative Priors in Bayesian Analyses
Throughout the last two decades, Bayesian statistical methods have proliferated throughout ecology and evolution. Numerous previous references established both philosophical and computational guidelines for implementing Bayesian methods. However, protocols for incorporating prior information, the defining characteristic of Bayesian philosophy, are nearly nonexistent in the ecological literature. Here, I hope to encourage the use of weakly informative priors in ecology and evolution by providing a ‘consumer\u27s guide’ to weakly informative priors. The first section outlines three reasons why ecologists should abandon noninformative priors: 1) common flat priors are not always noninformative, 2) noninformative priors provide the same result as simpler frequentist methods, and 3) noninformative priors suffer from the same high type I and type M error rates as frequentist methods. The second section provides a guide for implementing informative priors, wherein I detail convenient ‘reference’ prior distributions for common statistical models (i.e. regression, ANOVA, hierarchical models). I then use simulations to visually demonstrate how informative priors influence posterior parameter estimates. With the guidelines provided here, I hope to encourage the use of weakly informative priors for Bayesian analyses in ecology. Ecologists can and should debate the appropriate form of prior information, but should consider weakly informative priors as the new ‘default’ prior for any Bayesian model
Markov Chain Monte Carlo joint analysis of Chandra X-ray imaging spectroscopy and Sunyaev-Zeldovich Effect data
X-ray and Sunyaev-Zeldovich Effect data can be combined to determine the
distance to galaxy clusters. High-resolution X-ray data are now available from
the Chandra Observatory, which provides both spatial and spectral information,
and Sunyaev-Zeldovich Effect data were obtained from the BIMA and OVRO arrays.
We introduce a Markov chain Monte Carlo procedure for the joint analysis of
X-ray and Sunyaev-Zeldovich Effect data. The advantages of this method are the
high computational efficiency and the ability to measure simultaneously the
probability distribution of all parameters of interest, such as the spatial and
spectral properties of the cluster gas and also for derivative quantities such
as the distance to the cluster. We demonstrate this technique by applying it to
the Chandra X-ray data and the OVRO radio data for the galaxy cluster Abell
611. Comparisons with traditional likelihood-ratio methods reveal the
robustness of the method. This method will be used in follow-up papers to
determine the distances to a large sample of galaxy clusters.Comment: ApJ accepted, scheduled for ApJ 10 October 2004, v614 issue. Title
changed, added more convergence diagnostic tests, Figure 7 converted to lower
resolution for easier download, other minor change
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