QU-fitting is a model-fit method to reproduce the model of the Faraday Dispersion Function (FDF or Faraday spectrum), which is a probability distribution function of polarized intensity in Faraday depth space. In order to find the best-fit parameters of the model FDF, we adopt the Markov Chain Monte Carlo (MCMC) algorithm using Geweke’s convergence diagnostics. Akaike and Bayesian Information Criteria (AIC and BIC, respectively) are used to select the best model from several FDF fitting models. In this paper, we investigate the performance of the standard QU-fitting algorithm quantitatively by simulating spectro-polarimetric observations of two Faraday complex sources located along the same Line Of Sight (LOS), varying the gap between two sources in Faraday depth space and their widths, systematically. We fix the frequency bandwidth in 700–1800 MHz and make mock polarized spectra with a high Signal-to-Noise ratio (S/N). We prepare four FDF models for the fitting by changing the number of model parameters and test the correctness of MCMC and AIC/BIC. We find that the combination of MCMC and AIC/BIC works well for parameter estimation and model selection in the cases where the sources have widths smaller than 1/4 Full Width at Half Maximum (FWHM) and a gap larger than one FWHM in Faraday depth space. We note that when two sources have a gap of five FWHM in Faraday depth space, MCMC tends to be trapped in a local maximum likelihood compared to other situations.
Estimation of nonparametric ordinal logistic regression model using local maximum likelihood estimation
