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

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

Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $\Omega$ 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

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 $\Omega_M$ and $\Omega_\Lambda$, 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 $\Omega_M$ and $\Omega_\Lambda$ 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 $H_0$, 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

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 $\alpha$ 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: $\alpha = - 0.75^{+4.04}_{-0.24}$, $H_0=65.00^{+1.77}_{-1.75}$, $\Omega_{k0} = - 0.77^{+1.14}_{-5.94}$, $\Omega_{m0} = 0.00^{+1.95}_{-0.00}$, $\Omega_{c0} = 1.36^{+5.36}_{-0.85}$, $\bar A = 1.000^{+0.000}_{-0.534}$. Through the same analysis the specific case of the ordinary Chaplygin gas model (CGM), for which $\alpha = 1$, is studied. In this case, there are now four free parameters and the predictions for them are: $H_0 = 65.01^{+1.81}_{-1.71}$, $\Omega_{k0} = - 2.73^{+1.53}_{-0.97}$, $\Omega_{m0} = 0.00^{+1.22}_{-0.00}$, $\Omega_{c0} = 1.34^{+0.94}_{-0.70}$, $\bar A = 1.000^{+0.000}_{-0.270}$. To complete the analysis the $\Lambda$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 $\alpha = 1$ is far from been ruled out, and it is even preferred in some particular cases. In most of the cases the $\Lambda$CDM is disfavoured with respect to GCGM and CGM.Comment: 23 pages, LaTeX 2e, 6 tables, 38 EPS figures, uses graphic

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 $(E/E_0)^\alpha e^{-(\alpha+1)E/E_0}$ where $\alpha$ plays the role of a spectral index. This simple representation not only allows one to fit the total energy $E_{\rm tot}$ emitted in $\bar\nu_e$ 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 $E_{\rm tot}$ only if one fixes a prior value for $\alpha$. 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

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

Statistical Analysis of Spectral Line Candidates in Gamma-Ray Burst GRB870303

The Ginga data for the gamma-ray burst GRB870303 exhibit low-energy dips in two temporally distinct spectra, denoted S1 and S2. S1, spanning 4 s, exhibits a single line candidate at ~ 20 keV, while S2, spanning 9 s, exhibits apparently harmonically spaced line candidates at ~ 20 and 40 keV. We evaluate the statistical evidence for these lines, using phenomenological continuum and line models which in their details are independent of the distance scale to gamma-ray bursts. We employ the methodologies based on both frequentist and Bayesian statistical inference that we develop in Freeman et al. (1999b). These methodologies utilize the information present in the data to select the simplest model that adequately describes the data from among a wide range of continuum and continuum-plus-line(s) models. This ensures that the chosen model does not include free parameters that the data deem unnecessary and that would act to reduce the frequentist significance and Bayesian odds of the continuum-plus-line(s) model. We calculate the significance of the continuum-plus-line(s) models using the Chi-Square Maximum Likelihood Ratio test. We describe a parametrization of the exponentiated Gaussian absorption line shape that makes the probability surface in parameter space better-behaved, allowing us to estimate analytically the Bayesian odds. The significance of the continuum-plus-line models requested by the S1 and S2 data are 3.6 x 10^-5 and 1.7 x 10^-4 respectively, with the odds favoring them being 114:1 and 7:1. We also apply our methodology to the combined (S1+S2) data. The significance of the continuum-plus-lines model requested by the combined data is 4.2 x 10^-8, with the odds favoring it being 40,300:1.Comment: LaTeX2e (aastex.cls included); 41 pages text, 10 figures (on 11 pages); accepted by ApJ (to be published 1 Nov 1999, v. 525

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