Mathematics – Probability
Scientific paper
May 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aas...21640402i&link_type=abstract
American Astronomical Society, AAS Meeting #216, #404.02; Bulletin of the American Astronomical Society, Vol. 41, p.899
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 two RHESSI spectra, one from the X1.9 flare of 23 July 2002 and the other from the X4.8 flare of 19 January 2005, as an isothermal component plus a non-thermal bremsstrahlung photon spectrum produced in thick-target interactions by an electron distribution that is a double power law above a low energy cutoff. Each model has seven parameters. The parameter and error estimates from the Bayesian/MCMC approach are compared to two conventional fitting and error estimation techniques, Monte Carlo and chi-squared mapping.
We find that the Bayesian/MCMC approach estimates that the low energy cutoff of the 19 January 2005 spectrum is in the range 98-114 keV with 95% probability, in agreement with conventional analyses. For the 23 July 2002 spectrum, the Bayesian/MCMC approach finds a 95% probability that the low energy cutoff is below 32 keV, and that the probability distribution is approximately flat below 25 keV, indicating that there is insufficient information to further define the low energy cutoff energy below 25 keV, in intuitive agreement with expectations from examining the inferred photon flux which begins to be thermally dominated around 25-30 keV. In contrast with this expectation, the Monte Carlo technique yields a peaked low energy cutoff frequency distribution, with 95% of the distribution in the range 24-35 keV. Chi-squared mapping gives a 95% probability upper limit of 33 keV.
These results are explained in terms of the relative location of the low energy cutoff in the electron spectrum compared to the thermal contribution and the way each of the three methods explore the parameter search space.
Dennis Brian R.
Holman Gordon D.
Ireland Jack
Schwartz Richard A.
Tolbert Kimberley A.
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