MCMC estimation of SED model parameters using multi- wavelength data of the blazar Mrk 421

The spectral energy distributions (SEDs) of blazars are dominated by synchrotron and inverse Compton radiation. The origin of blazar variability can be investigated from the time variation of the SEDs. In the present study, we used Markov chain Monte Carlo (MCMC) method to estimate the optimal model parameters of SEDs and their uncertainties. Our experiments using artificial data demonstrate that at least one prior probability is required to uniquely determine the solution. We used simultaneous observations of Mrk 421 with Fermi-LAT, Swift-XRT, and the 1.5-m optical telescope, Kanata from 2009 to 2011 reported in Itoh et al. (2015). We succeeded in estimating the optimal parameters and their uncertainties by using the prior probability of the variation time-scale and Doppler factor. We found that the power-law index of the electron energy distribution shows a clear positive correlation with the X-ray flux even if the uncertainties are considered.