A powerful method to measure the mass profile of a galaxy is through the velocities of tracer particles distributed through its halo. Transforming this kind of data accurately to a mass profile , however, is not a trivial problem. In particular, limited or incomplete data may substantially affect the analysis. In this paper we develop a Bayesian method to deal with incomplete data effectively; we have a hybrid-Gibbs sampler that treats the unknown velocity components of tracers as parameters in the model. We explore the effectiveness of our model using simulated data and then apply our method to the Milky Way (MW) using velocity and position data from globular clusters and dwarf galaxies. We find that, in general, missing velocity components have little effect on the total mass estimate. However, the results are quite sensitive to the outer cluster Pal 3. Using a basic Hernquist model with an isotropic velocity dispersion, we obtain credible regions for the cumulative mass profile of the MW and provide estimates for the model parameters with 95% Bayesian credible intervals. The mass contained within 260 kpc is , with a 95% credible interval of . The Hernquist parameters for the total mass and scale radius are and kpc, where the uncertainties span the 95% credible intervals. The code we developed for this work, Galactic Mass Estimator (GME), will be available as an open source package in the R Project for Statistical Computing.
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机译：一种测量星系质量分布的有效方法是通过通过其晕圈分布的示踪剂粒子的速度。然而，将这类数据准确地转换为质量轮廓并不是一个小问题。特别是，有限或不完整的数据可能会严重影响分析。在本文中，我们开发了一种贝叶斯方法来有效地处理不完整的数据。我们有一个混合式Gibbs采样器，将示踪剂的未知速度分量作为模型中的参数进行处理。我们使用模拟数据探索模型的有效性，然后使用来自球状星团和矮星系的速度和位置数据将我们的方法应用于银河系（MW）。我们发现，总的来说，缺少速度分量对总质量估计几乎没有影响。但是，结果对外部簇Pal 3相当敏感。使用具有各向同性速度弥散的基本Hernquist模型，我们获得了MW累积质量分布的可靠区域，并提供了具有95％贝叶斯可信区间的模型参数的估计值。包含在260 kpc之内的质量为95％，可信区间为。总质量和标度半径的Hernquist参数为和kpc，其中不确定性跨越95％可信区间。我们为这项工作开发的代码Galactic Mass Estimator（GME）将作为R包提供给统计计算的R项目。
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