Bayesian Analysis of RHESSI Flare Data: Effect of Prior Information on Determining the Low-energy Cutoff and the Total Electron Content

Details Bayesian Analysis of RHESSI Flare Data: Effect of Prior Information on Determining the Low-energy Cutoff and the Total Electron Content Bayesian Analysis of RHESSI Flare Data: Effect of Prior Information on Determining the Low-energy Cutoff and the Total Electron Content

May 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011spd....42.2228i&link_type=abstract

American Astronomical Society, SPD meeting #42, #22.28; Bulletin of the American Astronomical Society, Vol. 43, 2011

Mathematics

Probability

Scientific paper

We use a Bayesian/Markov chain Monte Carlo (MCMC) posterior analysis to determine credible intervals (error estimates) to the parameter values of emission models. We model a RHESSI spectrum from the X1.9 flare of 23 July 2002 as an isothermal component plus a non-thermal bremsstrahlung photon spectrum produced in thin-target interactions by an electron distribution that is a double power law above a low energy cutoff.
The flare-injected electron distribution models mentioned above are subject to a low-energy cutoff. The location of this low-energy cutoff is not known precisely since the signal-to-noise ratio of the photons due to the non-thermal spectrum compared to the photons due to the thermal spectrum is small at the energies where the low-energy cutoff is thought to be. This parameter is of particular interest since it is a key component in determining the total electron content of flares. Bayesian data analysis allow one to include information (priors) on the likely value of parameters. Priors force one to explicitly quantify the expectations of the range and behavior of parameter values in a model. Credible intervals to the model parameter values (derived via Bayesian/Markov chain Monte Carlo (MCMC) posterior analysis) therefore include the effect of this prior information. In analyzing flares, priors allow one to explicitly quantify the expected values of parameters in flare models.
It is found that changing the prior of the total integrated electron flux model parameter from a flat prior (all values have equal probability) to a Jeffreys prior (orders of magnitude of the parameter value have equal probability) enhances peaks in the probability distribution of the low-energy cutoff below 25 keV. This prior-dependence suggests weak evidence for their actual presence. We find the most probable total electron content (along with its 68% and 95% credible interval) given the model flare spectra used.

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