False-alarm probability in relation to over-sampled power spectra, with application to Super-Kamiokande solar neutrino data

The term "false-alarm probability" denotes the probability that at least one out of M independent power values in a prescribed search band of a power spectrum computed from a white-noise time series is expected to be as large as or larger than a given value. The usual formula is based on the assumption that powers are distributed exponentially, as one expects for power measurements of normally distributed random noise. However, in practice one typically examines peaks in an over-sampled power spectrum. It is therefore more appropriate to compare the strength of a particular peak with the distribution of peaks in over-sampled power spectra derived from normally distributed random noise. We show that this leads to a formula for the false-alarm probability that is more conservative than the familiar formula. We also show how to combine these results with a Bayesian method for estimating the probability of the null hypothesis (that there is no oscillation in the time series), and we discuss as an example the application of these procedures to Super-Kamiokande solar neutrino data

Attributes of GRB Pulses: Bayesian Blocks Analysis of TTE Data; a Microburst in GRB 920229

Bayesian Blocks is a new time series algorithm for detecting localized structures (spikes or shots), revealing pulse shapes, and generally characterizing intensity variations. It maps raw counting data into a maximum likelihood piecewise constant representation of the underlying signal. This bin-free method imposes no lower limit on measurable time scales. Applied to BATSE TTE data, it reveals the shortest know burst structure -- a spike superimposed on the main burst in GRB 920229 = Trigger 1453, with rise and decay timescales ~ few 100 microseconds.Comment: 5 pages, 2 figures; presented at the 4th Huntsville Gamma-ray Burst Symposiu

Joint segmentation of multivariate astronomical time series : bayesian sampling with a hierarchical model

Astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series. This paper approaches such problems using Bayesian priors to represent relationships between signals with various degrees of certainty, and not just rigid constraints. The segmentation is conducted by using a hierarchical Bayesian approach to a piecewise constant Poisson rate model. A Gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters. Results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm

Structure in Galaxy Distribution. III. Fourier Transforming the Universe

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. However we concentrate on the less often studied Fourier phase spectrum, a simple and general framework for characterizing non-Gaussianity, more easily interpretable than the tangled, incomplete multi-point methods conventionally used. No significant signature of non-Gaussianity has been found in the relatively small data set analyzed, but we identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.Comment: 34 pages, 14 figures, Paper III in the series; second major revision. NB some pdf viewers may show spurious patterns in Fig. 6-1