1,749 research outputs found
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
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