基于贝叶斯推断的脉冲星偏振位置角拟合算法

摘要

For pulsar emission beams, a widely used relationship between the polarization position angle (PPA) and the pulse phase is given by the Rotation Vector Model (RVM). Current methods of fitting the PPA with RVM are on the basis of Levenberg-Marquardt nonlinear fitting or grid searching algorithms, however, they suffer from inefficiency and overfitting problems. A Markov Chain Monte Carlo (MCMC) algorithm on the basis of Bayesian inference is developed and applied to the fitting of PPA for 10 pulsars, which have been studied in literature with old methods. It is shown that the MCMC algorithm can not only obtain consistent results as those in literatures, but also have advantages in efficiency, the abilities of overcoming over-fitting and estimating the uncertainties of model parameters.%脉冲星辐射束的偏振位置角与相位的关系可用旋转矢量模型(RVM)描述，现有的Levenberg-Marquardt非线性拟合和格点搜寻算法对RVM的拟合存在效率低、易过拟合等问题。本文发展了一套基于贝叶斯推断的马尔可夫链蒙特卡洛算法(MCMC)，并用该方法对已有文献中的10颗脉冲星偏振位置角进行了拟合。结果表明， MCMC算法不仅能得到与已有文献一致的结果，而且该算法具有高效、不易过拟合、能更好地估计参数的可信度区间等优点。