arXiv subjects

Thomas J. Loredo

Publications and source records attributed to Thomas J. Loredo.

At least 37 records · Page 2Linked to original sources

arXiv2013

A template for describing intrinsic GRB pulse shapes

A preliminary study of a set of well-isolated pulses in GRB light curves indicates that simple pulse models, with smooth and monotonic pulse rise and decay regions, are inadequate. Examining the residuals of fits of pulses to such models suggests the following patterns of departure from the smooth pulse model of Norris et al. (2005): A Precursor Shelf occurs prior to or concurrent with the exponential Rapid Rise. The pulse reaches maximum intensity at the Peak Plateau, then undergoes a Rapid Decay. The decay changes into an Extended Tail. Pulses are almost universally characterized by hard-to-soft evolution, arguing that the new pulse features reflect a single physical phenomenon, rather than artifacts of pulse overlap.

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arXiv2012

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.

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arXiv2012

On the future of astrostatistics: statistical foundations and statistical practice

This paper summarizes a presentation for a panel discussion on "The Future of Astrostatistics" held at the Statistical Challenges in Modern Astronomy V conference at Pennsylvania State University in June 2011. I argue that the emerging needs of astrostatistics may both motivate and benefit from fundamental developments in statistics. I highlight some recent work within statistics on fundamental topics relevant to astrostatistical practice, including the Bayesian/frequentist debate (and ideas for a synthesis), multilevel models, and multiple testing. As an important direction for future work in statistics, I emphasize that astronomers need a statistical framework that explicitly supports unfolding chains of discovery, with acquisition, cataloging, and modeling of data not seen as isolated tasks, but rather as parts of an ongoing, integrated sequence of analyses, with information and uncertainty propagating forward and backward through the chain. A prototypical example is surveying of astronomical populations, where source detection, demographic modeling, and the design of survey instruments and strategies all interact.

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arXiv2012

Commentary on Bayesian coincidence assessment (cross-matching)

This paper is an invited commentary on Tamas Budavari's presentation, "On statistical cross-identification in astronomy," for the Statistical Challenges in Modern Astronomy V conference held at Pennsylvania State University in June 2011. I begin with a brief review of previous work on probabilistic (Bayesian) assessment of directional and spatio-temporal coincidences in astronomy (e.g., cross-matching or cross-identification of objects across multiple catalogs). Then I discuss an open issue in the recent innovative work of Budavari and his colleagues on large-scale probabilistic cross-identification: how to assign prior probabilities that play an important role in the analysis. With a simple toy problem, I show how Bayesian multilevel modeling (hierarchical Bayes) provides a principled framework that justifies and generalizes pragmatic rules of thumb that have been successfully used by Budavari's team to assign priors.

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arXiv2012

Transit and Eclipse Analyses of Exoplanet HD 149026b Using BLISS Mapping

The dayside of HD 149026b is near the edge of detectability by the Spitzer Space Telescope. We report on eleven secondary-eclipse events at 3.6, 4.5, 3 x 5.8, 4 x 8.0, and 2 x 16 microns plus three primary-transit events at 8.0 microns. The eclipse depths from jointly-fit models at each wavelength are 0.040 +/- 0.003% at 3.6 microns, 0.034 +/- 0.006% at 4.5 microns, 0.044 +/- 0.010% at 5.8 microns, 0.052 +/- 0.006% at 8.0 microns, and 0.085 +/- 0.032% at 16 microns. Multiple observations at the longer wavelengths improved eclipse-depth signal-to-noise ratios by up to a factor of two and improved estimates of the planet-to-star radius ratio (Rp/Rs = 0.0518 +/- 0.0006). We also identify no significant deviations from a circular orbit and, using this model, report an improved period of 2.8758916 +/- 0.0000014 days. Chemical-equilibrium models find no indication of a temperature inversion in the dayside atmosphere of HD 149026b. Our best-fit model favors large amounts of CO and CO2, moderate heat redistribution (f=0.5), and a strongly enhanced metallicity. These analyses use BiLinearly-Interpolated Subpixel Sensitivity (BLISS) mapping, a new technique to model two position-dependent systematics (intrapixel variability and pixelation) by mapping the pixel surface at high resolution. BLISS mapping outperforms previous methods in both speed and goodness of fit. We also present an orthogonalization technique for linearly-correlated parameters that accelerates the convergence of Markov chains that employ the Metropolis random walk sampler. The electronic supplement contains light-curve files and supplementary figures.

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arXiv2012

Sines, steps and droplets: Semiparametric Bayesian modeling of arrival time series

I describe ongoing work developing Bayesian methods for flexible modeling of arrival time series data without binning, aiming to improve detection and measurement of X-ray and gamma-ray pulsars, and of pulses in gamma-ray bursts. The methods use parametric and semiparametric Poisson point process models for the event rate, and by design have close connections to conventional frequentist methods currently used in time-domain astronomy.

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arXiv2011

Spitzer Secondary Eclipses of WASP-18b

The transiting exoplanet WASP-18b was discovered in 2008 by the Wide Angle Search for Planets (WASP) project. The Spitzer Exoplanet Target of Opportunity Program observed secondary eclipses of WASP-18b using Spitzer's Infrared Array Camera (IRAC) in the 3.6 micron and 5.8 micron bands on 2008 December 20, and in the 4.5 micron and 8.0 micron bands on 2008 December 24. We report eclipse depths of 0.30 +/- 0.02%, 0.39 +/- 0.02%, 0.37 +/- 0.03%, 0.41 +/- 0.02%, and brightness temperatures of 3100 +/- 90, 3310 +/- 130, 3080 +/- 140 and 3120 +/- 110 K in order of increasing wavelength. WASP-18b is one of the hottest planets yet discovered - as hot as an M-class star. The planet's pressure-temperature profile most likely features a thermal inversion. The observations also require WASP-18b to have near-zero albedo and almost no redistribution of energy from the day-side to the night side of the planet.

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arXiv2011

Rotating Stars and Revolving Planets: Bayesian Exploration of the Pulsating Sky

I describe ongoing work on development of Bayesian methods for exploring periodically varying phenomena in astronomy, addressing two classes of sources: pulsars, and extrasolar planets (exoplanets). For pulsars, the methods aim to detect and measure periodically varying signals in data consisting of photon arrival times, modeled as non-homogeneous Poisson point processes. For exoplanets, the methods address detection and estimation of planetary orbits using observations of the reflex motion "wobble" of a host star, including adaptive scheduling of observations to optimize inferences.

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arXiv2010

On the Orbit of Exoplanet WASP-12b

We observed two secondary eclipses of the exoplanet WASP-12b using the Infrared Array Camera on the Spitzer Space Telescope. The close proximity of WASP-12b to its G-type star results in extreme tidal forces capable of inducing apsidal precession with a period as short as a few decades. This precession would be measurable if the orbit had a significant eccentricity, leading to an estimate of the tidal Love number and an assessment of the degree of central concentration in the planetary interior. An initial ground-based secondary eclipse phase reported by Lopez-Morales et al. (0.510 +/- 0.002) implied eccentricity at the 4.5 sigma level. The spectroscopic orbit of Hebb et al. has eccentricity 0.049 +/- 0.015, a 3 sigma result, implying an eclipse phase of 0.509 +/- 0.007. However, there is a well documented tendency of spectroscopic data to overestimate small eccentricities. Our eclipse phases are 0.5010 +/- 0.0006 (3.6 and 5.8 microns) and 0.5006 +/- 0.0007 (4.5 and 8.0 microns). An unlikely orbital precession scenario invoking an alignment of the orbit during the Spitzer observations could have explained this apparent discrepancy, but the final eclipse phase of Lopez-Morales et al. (0.510 -0.006 / +0.007) is consistent with a circular orbit at better than 2 sigma. An orbit fit to all the available transit, eclipse, and radial-velocity data indicates precession at <1 sigma; a non-precessing solution fits better. We also comment on analysis and reporting for Spitzer exoplanet data in light of recent re-analyses.

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arXiv2009

Introduction to papers on astrostatistics

We are pleased to present a Special Section on Statistics and Astronomy in this issue of the The Annals of Applied Statistics. Astronomy is an observational rather than experimental science; as a result, astronomical data sets both small and large present particularly challenging problems to analysts who must make the best of whatever the sky offers their instruments. The resulting statistical problems have enormous diversity. In one problem, one may have to carefully quantify uncertainty in a hard-won, sparse data set; in another, the sheer volume of data may forbid a formally optimal analysis, requiring judicious balancing of model sophistication, approximations, and clever algorithms. Often the data bear a complex relationship to the underlying phenomenon producing them, much in the manner of inverse problems.

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arXiv2004

Bayesian Adaptive Exploration

I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data and predict future data, and Bayesian decision theory to identify which new observations would teach us the most. When the goal of the experiment is simply to make inferences, the framework identifies a computationally efficient iterative ``maximum entropy sampling'' strategy as the optimal strategy in settings where the noise statistics are independent of signal properties. Results of applying the method to two ``toy'' problems with simulated data--measuring the orbit of an extrasolar planet, and locating a hidden one-dimensional object--show the approach can significantly improve observational efficiency in settings that have well-defined nonlinear models. I conclude with a list of open issues that must be addressed to make Bayesian adaptive exploration a practical and reliable tool for optimizing scientific exploration.

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arXiv2004

Accounting for Source Uncertainties in Analyses of Astronomical Survey Data

I discuss an issue arising in analyzing data from astronomical surveys: accounting for measurement uncertainties in the properties of individual sources detected in a survey when making inferences about the entire population of sources. Source uncertainties require the analyst to introduce unknown ``incidental'' parameters for each source. The number of parameters thus grows with the size of the sample, and standard theorems guaranteeing asymptotic convergence of maximum likelihood estimates fail in such settings. From the Bayesian point of view, the missing ingredient in such analyses is accounting for the volume in the incidental parameter space via marginalization. I use simple simulations, motivated by modeling the distribution of trans-Neptunian objects surveyed in the outer solar system, to study the effects of source uncertainties on inferences. The simulations show that current non-Bayesian methods for handling source uncertainties (ignoring them, or using an ad hoc incidental parameter integration) produce incorrect inferences, with errors that grow more severe with increasing sample size. In contrast, accounting for source uncertainty via marginalization leads to sound inferences for any sample size.

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arXiv2001

Search for high-frequency periodicities in time-tagged event data from gamma ray bursts and soft gamma repeaters

We analyze the Time-Tagged Event (TTE) data from observations of gamma ray bursts (GRBs) and soft gamma repeaters (SGRs) by the Burst and Transient Source Experiment (BATSE). These data provide the best available time resolution for GRBs and SGRs. We have performed an extensive search for weak periodic signals in the frequency range 400 Hz to 2500 Hz using the burst records for 2203 GRBs and 152 SGR flares. The study employs the Rayleigh power as a test statistic to evaluate the evidence for periodic emissions. We find no evidence of periodic emissions from these events at these frequencies. In all but a very few cases the maximum power values obtained are consistent with what would be expected by chance from a non-periodic signal. In those few instances where there is marginal evidence for periodicity there are problems with the data that cast doubt on the reality of the signal. For classical GRBs, the largest Rayleigh power occurs in bursts whose TTE data appear to be corrupted. For SGRs, our largest Rayleigh power, with a significance of 1%, occurs in one record for SGR 1900+14 (at 2497 Hz), and in no other outbursts associated with this source; we thus consider it unlikely to represent detection of a real periodicity. From simulations, we deduce that the Rayleigh test would have detected significant oscillations with relative amplitude ~10% about half the time. Thus, we conclude that high frequency oscillations, if present, must have small relative amplitudes.

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arXiv2001

Bayesian analysis of neutrinos observed from supernova SN 1987A

We present a Bayesian analysis of the energies and arrival times of the neutrinos from supernova SN 1987A detected by the Kamiokande II, IMB, and Baksan detectors, and find strong evidence for two components in the neutrino signal: a long time scale component from thermal Kelvin-Helmholtz cooling of the nascent neutron star, and a brief (~< 1 s), softer component similar to that expected from emission by accreting material in the delayed supernova scenario. In the context of this model, we show that the data constrain the electron antineutrino rest mass to be less than 5.7 eV with 95% probability. Our analysis takes advantage of significant advances that have occured in the years since the detections in both our understanding of the supernova mechanism and our ability to analyze sparse data. As a result there are substantial differences between our inferences and those found in earlier studies. We find that two-component models for the neutrino signal make the data >100 times more probable than single-component models. In addition, the radius and binding energy of the nascent neutron star implied by single-component models deviates significantly from the values predicted by current neutron star models, whereas those implied by models with an accretion component are in complete agreement with the predictions. As a result, two-component models are hundreds to thousands of times more probable than single-component models. The neutrino data thus provide the first direct observational evidence in favor of the delayed supernova scenario over the prompt scenario. (Abridged abstract)

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arXiv1999

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 $Ω_M$ and $Ω_Λ$, 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 $Ω_M$ and $Ω_Λ$ 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.

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arXiv1998

Pencil-Beam Surveys for Faint Trans-Neptunian Objects

We have conducted pencil-beam searches for outer solar system objects to a limiting magnitude of R ~ 26. Five new trans-neptunian objects were detected in these searches. Our combined data set provides an estimate of ~90 trans-neptunian objects per square degree brighter than ~ 25.9. This estimate is a factor of 3 above the expected number of objects based on an extrapolation of previous surveys with brighter limits, and appears consistent with the hypothesis of a single power-law luminosity function for the entire trans-neptunian region. Maximum likelihood fits to all self-consistent published surveys with published efficiency functions predicts a cumulative sky density Sigma(<R) obeying log10(Sigma) = 0.76(R-23.4) objects per square degree brighter than a given magnitude R.

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arXiv1997

Bayesian Analysis of the Polarization of Distant Radio Sources: Limits on Cosmological Birefringence

A recent study of the rotation of the plane of polarization of light from 160 cosmological sources claims to find significant evidence for cosmological anisotropy. We point out methodological weaknesses of that study, and reanalyze the same data using Bayesian methods that overcome these problems. We find that the data always favor isotropic models for the distribution of observed polarizations over counterparts that have a cosmological anisotropy of the type advocated in the earlier study. Although anisotropic models are not completely ruled out, the data put strong lower limits on the length scale $λ$ (in units of the Hubble length) associated with the anisotropy; the lower limits of 95% credible regions for $λ$ lie between 0.43 and 0.62 in all anisotropic models we studied, values several times larger than the best-fit value of $λ\approx 0.1$ found in the earlier study. The length scale is not constrained from above. The vast majority of sources in the data are at distances closer than 0.4 Hubble lengths (corresponding to a redshift of $\approx$0.8); the results are thus consistent with there being no significant anisotropy on the length scale probed by these data.

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arXiv1997

Inferring the Spatial and Energy Distribution of Gamma Ray Burst Sources. II. Isotropic Models

We use Bayesian methods to analyze the distribution of gamma ray burst intensities reported in the Third BATSE Catalog (3B catalog) of gamma ray bursts, presuming the distribution of burst sources (``bursters'') is isotropic. We study both phenomenological and cosmological source distribution models, using Bayes's theorem both to infer unknown parameters in the models, and to compare rival models. We analyze the distribution of the time-averaged peak photon number flux, F, measured on both 64 ms and 1024 ms time scales, performing the analysis of data based on each time scale independently. Several of our findings differ from those of previous analyses that modeled burst detection less completely. In particular, we find that the width of the intrinsic luminosity function for bursters is unconstrained, and the luminosity function of the actually observed bursts can be extremely broad, in contrast to the findings of all previous studies. Useful constraints probably require observation of bursts significantly fainter than those visible to BATSE. We also find that the 3B peak flux data do not usefully constrain the redshifts of burst sources; useful constraints require the analysis of data beyond that in the 3B catalog (such as burst time histories), or data from brighter bursts than have been seen by BATSE (such as those observed by the Pioneer Venus Orbiter). In addition, we find that an accurate understanding of the peak flux distributions reported in the 3B almost certainly requires consideration of data on the temporal and spectral properties of bursts beyond that reported in the 3B catalog, and more sophisticated modeling than has so far been attempted.

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