279 research outputs found
Covariant Symmetry Classifications for Observables of Cosmological Birefringence
Polarizations of electromagnetic waves from distant galaxies are known to be
correlated with the source orientations. These quantities have been used to
search for signals of cosmological birefringence. We review and classify
transformation properties of the polarization and source orientation
observables. The classifications give a firm foundation to certain practices
which have sprung up informally in the literature. Transformations under parity
play a central role, showing that parity violation in emission or in the
subsequent propagation is an observable phenomenon. We also discuss statistical
measures, correlations and distributions which transform properly and which can
be used for systematic data analysis.Comment: 8 pages, revtex, 1 postscript figur
Getting the Measure of the Flatness Problem
The problem of estimating cosmological parameters such as from noisy
or incomplete data is an example of an inverse problem and, as such, generally
requires a probablistic approach. We adopt the Bayesian interpretation of
probability for such problems and stress the connection between probability and
information which this approach makes explicit.
This connection is important even when information is ``minimal'' or, in
other words, when we need to argue from a state of maximum ignorance. We use
the transformation group method of Jaynes to assign minimally--informative
prior probability measure for cosmological parameters in the simple example of
a dust Friedman model, showing that the usual statements of the cosmological
flatness problem are based on an inappropriate choice of prior. We further
demonstrate that, in the framework of a classical cosmological model, there is
no flatness problem.Comment: 11 pages, submitted to Classical and Quantum Gravity, Tex source
file, no figur
Likelihood Analysis of Repeating in the BATSE Catalogue
I describe a new likelihood technique, based on counts-in-cells statistics,
that I use to analyze repeating in the BATSE 1B and 2B catalogues. Using the 1B
data, I find that repeating is preferred over non-repeating by 4.3:1 odds, with
a well-defined peak at 5-6 repetitions per source. I find that the post-1B data
are consistent with the repeating model inferred from the 1B data, after taking
into account the lower fraction of bursts with well-determined positions.
Combining the two data sets, I find that the odds favoring repeating over
non-repeating are almost unaffected at 4:1, with a narrower peak at 5
repetitions per source. I conclude that the data sets are consistent both with
each other and with repeating, and that for these data sets the odds favor
repeating.Comment: 5 pages including 3 encapsulated figures, as a uuencoded, gzipped,
Postscript file. To appear in Proc. of the 1995 La Jolla workshop ``High
Velocity Neutron Stars and Gamma-Ray Bursts'' eds. Rothschild, R. et al.,
AIP, New Yor
Bayesian astrostatistics: a backward look to the future
This perspective chapter briefly surveys: (1) past growth in the use of
Bayesian methods in astrophysics; (2) current misconceptions about both
frequentist and Bayesian statistical inference that hinder wider adoption of
Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian
modeling as a major future direction for research in Bayesian astrostatistics,
exemplified in part by presentations at the first ISI invited session on
astrostatistics, commemorated in this volume. It closes with an intentionally
provocative recommendation for astronomical survey data reporting, motivated by
the multilevel Bayesian perspective on modeling cosmic populations: that
astronomers cease producing catalogs of estimated fluxes and other source
properties from surveys. Instead, summaries of likelihood functions (or
marginal likelihood functions) for source properties should be reported (not
posterior probability density functions), including nontrivial summaries (not
simply upper limits) for candidate objects that do not pass traditional
detection thresholds.Comment: 27 pp, 4 figures. A lightly revised version of a chapter in
"Astrostatistical Challenges for the New Astronomy" (Joseph M. Hilbe, ed.,
Springer, New York, forthcoming in 2012), the inaugural volume for the
Springer Series in Astrostatistics. Version 2 has minor clarifications and an
additional referenc
Bayesian Analysis of the (Generalized) Chaplygin Gas and Cosmological Constant Models using the 157 gold SNe Ia Data
The generalized Chaplygin gas model (GCGM) contains 5 free parameters, here,
they are constrained through the type Ia supernovae data, i.e., the ``gold
sample'' of 157 supernovae data. Negative and large positive values for
are taken into account. The analysis is made by employing the Bayesian
statistics and the prediction for each parameter is obtained by marginalizing
on the remained ones. This procedure leads to the following predictions:
, , , , , . Through the same
analysis the specific case of the ordinary Chaplygin gas model (CGM), for which
, is studied. In this case, there are now four free parameters and
the predictions for them are: , , , , . To complete the
analysis the CDM, with its three free parameters, is considered. For
all these models, particular cases are considered where one or two parameters
are fixed. The age of the Universe, the deceleration parameter and the moment
the Universe begins to accelerate are also evaluated. The quartessence
scenario, is favoured. A closed (and in some cases a flat) and accelerating
Universe is also preferred. The CGM case is far from been ruled
out, and it is even preferred in some particular cases. In most of the cases
the CDM is disfavoured with respect to GCGM and CGM.Comment: 23 pages, LaTeX 2e, 6 tables, 38 EPS figures, uses graphic
Type Ia Supernovae, Evolution, and the Cosmological Constant
We explore the possible role of evolution in the analysis of data on SNe Ia
at cosmological distances. First, using a variety of simple sleuthing
techniques, we find evidence that the properties of the high and low redshift
SNe Ia observed so far differ from one another. Next, we examine the effects of
including simple phenomenological models for evolution in the analysis. The
result is that cosmological models and evolution are highly degenerate with one
another, so that the incorporation of even very simple models for evolution
makes it virtually impossible to pin down the values of and
, the density parameters for nonrelativistic matter and for the
cosmological constant, respectively. Moreover, we show that if SNe Ia evolve
with time, but evolution is neglected in analyzing data, then, given enough SNe
Ia, the analysis hones in on values of and which
are incorrect. Using Bayesian methods, we show that the probability that the
cosmological constant is nonzero (rather than zero) is unchanged by the SNe Ia
data when one accounts for the possibility of evolution, provided that we do
not discriminate among open, closed and flat cosmologies a priori. The case for
nonzero cosmological constant is stronger if the Universe is presumed to be
flat, but still depends sensitively on the degree to which the peak
luminosities of SNe Ia evolve as a function of redshift. The estimated value of
, however, is only negligibly affected by accounting for possible
evolution.Comment: 45 pages, 15 figures; accepted for publication in The Astrophysical
Journal. Minor revisions and clarifications made including addition of recent
reference
New analysis of the SN 1987A neutrinos with a flexible spectral shape
We analyze the neutrino events from the supernova (SN) 1987A detected by the
Kamiokande II (KII) and Irvine-Michigan-Brookhaven (IMB) experiments. For the
time-integrated flux we assume a quasi-thermal spectrum of the form
where plays the role of a
spectral index. This simple representation not only allows one to fit the total
energy emitted in and the average energy
, but also accommodates a wide range of shapes, notably
anti-pinched spectra that are broader than a thermal distribution. We find that
the pile-up of low-energy events near threshold in KII forces the best-fit
value for $\alpha$ to the lowest value of any assumed prior range. This applies
to the KII events alone as well as to a common analysis of the two data sets.
The preference of the data for an ``unphysical'' spectral shape implies that
one can extract meaningful values for and only
if one fixes a prior value for . The tension between the KII and IMB
data sets and theoretical expectations for is not resolved by
an anti-pinched spectrum.Comment: to appear in PRD (6 pages, 6 eps figures
Bayesian Constraints on theta_{13} from Solar and KamLAND Neutrino Data
We present the results of a Bayesian analysis of solar and KamLAND neutrino
data in the framework of three-neutrino mixing. We adopt two approaches for the
prior probability distribution of the oscillation parameters Delta m^2_{21},
sin^2 theta_{12}, sin^2 theta_{13}: 1) a traditional flat uninformative prior;
2) an informative prior which describes the limits on sin^2 theta_{13} obtained
in atmospheric and long-baseline accelerator and reactor neutrino experiments.
In both approaches, we present the allowed regions in the sin^2 theta_{13} -
Delta m^2_{21} and sin^2 theta_{12} - sin^2 theta_{13} planes, as well as the
marginal posterior probability distribution of sin^2 theta_{13}. We confirm the
1.2 sigma hint of theta_{13} > 0 found in hep-ph/0806.2649 from the analysis of
solar and KamLAND neutrino data. We found that the statistical significance of
the hint is reduced to about 0.8 sigma by the constraints on sin^2 theta_{13}
coming from atmospheric and long-baseline accelerator and reactor neutrino
data, in agreement with arXiv:0808.2016.Comment: 21 pages. Final version published in Phys. Rev. D 80 (2009) 05300
Avoiding selection bias in gravitational wave astronomy
When searching for gravitational waves in the data from ground-based
gravitational wave detectors it is common to use a detection threshold to
reduce the number of background events which are unlikely to be the signals of
interest. However, imposing such a threshold will also discard some real
signals with low amplitude, which can potentially bias any inferences drawn
from the population of detected signals. We show how this selection bias is
naturally avoided by using the full information from the search, considering
both the selected data and our ignorance of the data that are thrown away, and
considering all relevant signal and noise models. This approach produces
unbiased estimates of parameters even in the presence of false alarms and
incomplete data. This can be seen as an extension of previous methods into the
high false rate regime where we are able to show that the quality of parameter
inference can be optimised by lowering thresholds and increasing the false
alarm rate.Comment: 13 pages, 2 figure
The Virgo Alignment Puzzle in Propagation of Radiation on Cosmological Scales
We reconsider analysis of data on the cosmic microwave background on the
largest angular scales. Temperature multipoles of any order factor naturally
into a direct product of axial quantities and cosets. Striking coincidences
exist among the axes associated with the dipole, quadrupole, and octupole CMB
moments. These axes also coincide well with two other axes independently
determined from polarizations at radio and optical frequencies propagating on
cosmological scales. The five coincident axes indicate physical correlation and
anisotropic properties of the cosmic medium not predicted by the conventional
Big Bang scenario. We consider various mechanisms, including foreground
corrections, as candidates for the observed correlations. We also consider
whether the propagation anomalies may be a signal of ``dark energy'' in the
form of a condensed background field. Perhaps {\it light propagation} will
prove to be an effective way to look for the effects of {\it dark energy}.Comment: 24 pages, 4 figures, minor changes, no change in result or
conclusions. to appear in IJMP
- …