A statistical analysis of the observed perturbations in the density of stellar streams can in principle set stringent contraints on the mass function of dark matter subhaloes, which in turn can be used to constrain the mass of the dark matter particle. However, the likelihood of a stellar density with respect to the stream and subhaloes parameters involves solving an intractable inverse problem which rests on the integration of all possible forward realisations implicitly defined by the simulation model. In order to infer the subhalo abundance, previous analyses have relied on Approximate Bayesian Computation (ABC) together with domain-motivated but handcrafted summary statistics. Here, we introduce a likelihood-free Bayesian inference pipeline based on Amortised Approximate Likelihood Ratios (AALR), which automatically learns a mapping between the data and the simulator parameters and obviates the need to handcraft a possibly insufficient summary statistic. We apply the method to the simplified case where stellar streams are only perturbed by dark matter subhaloes, thus neglecting baryonic substructures, and describe several diagnostics that demonstrate the effectiveness of the new method and the statistical quality of the learned estimator.
翻译:对恒星流密度观察到的扰动进行统计分析,原则上可以对暗物质亚卤化物质的质量功能设定严格的对照,而暗物质亚卤化物质的质量功能又可以用来限制暗物质粒子的质量;然而,对流体和亚卤化物参数的恒星密度可能性涉及解决一个棘手的反向问题,它取决于模拟模型暗含的所有可能的前瞻性实现的整合。为了推断亚卤丰度,以往的分析依据的是Apviear Bayesian Comput (ABC) 以及以域为动力但手工制作的简要统计数据。在这里,我们采用了一种基于摊合近似近似相似性比率(AALR)的无概率贝氏推断管道,自动学习数据与模拟参数之间的映射图,并避免了手工艺可能不足的简要统计的必要性。我们将这种方法应用于一个简化的案例,在这个案例中,恒星流只被暗物质亚化,从而忽略了巴里基结构,并描述若干测量方法的有效性。