A Bayesian Multivariate Functional Dynamic Linear Model

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online

BATSE Gamma-Ray Burst Line Search: V. Probability of Detecting a Line in a Burst

The physical importance of the apparent discrepancy between the detections by pre-BATSE missions of absorption lines in gamma-ray burst spectra and the absence of a BATSE line detection necessitates a statistical analysis of this discrepancy. This analysis requires a calculation of the probability that a line, if present, will be detected in a given burst. However, the connection between the detectability of a line in a spectrum and in a burst requires a model for the occurrence of a line within a burst. We have developed the necessary weighting for the line detection probability for each spectrum spanning the burst. The resulting calculations require a description of each spectrum in the BATSE database. With these tools we identify the bursts in which lines are most likely to be detected. Also, by assuming a small frequency with which lines occur, we calculate the approximate number of BATSE bursts in which lines of various types could be detected. Lines similar to the Ginga detections can be detected in relatively few BATSE bursts; for example, in only ~20 bursts are lines similar to the GB 880205 pair of lines detectable. Ginga reported lines at ~20 and ~40 keV whereas the low energy cutoff of the BATSE spectra is typically above 20 keV; hence BATSE's sensitivity to lines is less than that of Ginga below 40 keV, and greater above. Therefore the probability that the GB 880205 lines would be detected in a Ginga burst rather than a BATSE burst is ~0.2. Finally, we adopted a more appropriate test of the significance of a line feature.Comment: 20 pages, AASTeX 4.0, 5 figures, Ap.J. in pres

Spectral Hardness Decay with Respect to Fluence in BATSE Gamma-Ray Bursts

We have analyzed the evolution of the spectral hardness parameter Epk as a function of fluence in gamma-ray bursts. We fit 41 pulses within 26 bursts with the trend reported by Liang & Kargatis (1996) which found that Epk decays exponentially with respect to photon fluence. We also fit these pulses with a slight modification of this trend, where Epk decays linearly with energy fluence. In both cases, we found the set of 41 pulses to be consistent with the trend. For the latter trend, which we believe to be more physical, the distribution of the decay constant is roughly log-normal, with a mean of 1.75 +/- 0.07 and a FWHM of 1.0 +/- 0.1. Regarding an earlier reported invariance in the decay constant among different pulses in a single burst, we found probabilities of 0.49 to 0.84 (depending on the test used) that such invariance would occur by coincidence, most likely due to the narrow distribution of decay constant values among pulses.Comment: 17 pages, 7 figure pages, 2 table pages, submitted to The Astrophysical Journa

Spatiotemporal mixed modeling of multi-subject task fMRI via method of moments

Estimating spatiotemporal models for multi-subject fMRI is computationally challenging. We propose a mixed model for localization studies with spatial random effects and time-series errors. We develop method-of-moment estimators that leverage population and spatial information and are scalable to massive datasets. In simulations, subject-specific estimates of activation are considerably more accurate than the standard voxel-wise general linear model. Our mixed model also allows for valid population inference. We apply our model to cortical data from motor and theory of mind tasks from the Human Connectome Project (HCP). The proposed method results in subject-specific predictions that appear smoother and less noisy than those from the popular single-subject univariate approach. In particular, the regions of motor cortex associated with a left-hand finger-tapping task appear to be more clearly delineated. Subject-specific maps of activation from task fMRI are increasingly used in pre-surgical planning for tumor removal and in locating targets for transcranial magnetic stimulation. Our findings suggest that using spatial and population information is a promising avenue for improving clinical neuroimaging

BATSE Gamma-Ray Burst Line Search: IV. Line Candidates from the Visual Search

We evaluate the significance of the line candidates identified by a visual search of burst spectra from BATSE's Spectroscopy Detectors. None of the candidates satisfy our detection criteria: an F-test probability less than 10^-4 for a feature in one detector and consistency among the detectors which viewed the burst. Most of the candidates are not very significant, and are likely to be fluctuations. Because of the expectation of finding absorption lines, the search was biased towards absorption features. We do not have a quantitative measure of the completeness of the search which would enable a comparison with previous missions. Therefore a more objective computerized search has begun.Comment: 18 pages AASTEX 4.0; 4 POSTSCRIPT figures on request from [email protected]

Evolution of the Low-Energy Photon Spectra in Gamma-Ray Bursts

We report evidence that the asymptotic low-energy power law slope alpha (below the spectral break) of BATSE gamma-ray burst photon spectra evolves with time rather than remaining constant. We find a high degree of positive correlation exists between the time-resolved spectral break energy E_pk and alpha. In samples of 18 "hard-to-soft" and 12 "tracking" pulses, evolution of alpha was found to correlate with that of the spectral break energy E_pk at the 99.7% and 98% confidence levels respectively. We also find that in the flux rise phase of "hard-to-soft" pulses, the mean value of alpha is often positive and in some bursts the maximum value of alpha is consistent with a value > +1. BATSE burst 3B 910927, for example, has a alpha_max equal to 1.6 +/- 0.3. These findings challenge GRB spectral models in which alpha must be negative of remain constant.Comment: 12 pages (including 6 figures), accepted to Ap