Approximate Bayesian computation for forward modeling in cosmology
Approximate Bayesian computation for forward modeling in cosmology
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DOI：
10.1088/1475-7516/2015/08/043
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发表时间：
2015-08-01
影响因子：
6.4
通讯作者：
Hasner, Caspar
中科院分区：
文献类型：
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作者：
Akeret, Joel;Refregier, Alexandre;Hasner, Caspar
贝叶斯推断经常用于宇宙学和天体物理学中，以从观测中获得对模型参数的约束。这种方法依赖于在给定模型参数选择的情况下计算数据的可能性的能力。然而，在许多实际情况下，由于非高斯误差、非线性测量过程或复杂的数据格式（如目录和地图），似然函数可能不可用或难以处理。在这些情况下，模拟数据集的模拟通常可以通过正向建模来进行。我们讨论了如何近似贝叶斯计算（ABC）可以在这些情况下，使用模拟数据集来获得近似的后验约束。该技术依赖于参数集的采样、量化观察和模拟之间的差异的距离度量以及压缩数据中的信息的汇总统计。我们首先回顾ABC的原则，并讨论其实施使用人口蒙特-卡罗（PMC）算法和马氏距离度量。我们使用高斯玩具模型来测试实现的性能。然后，我们应用ABC技术的实际情况下，宽场宇宙学调查的图像模拟的校准。我们发现，ABC分析是能够提供可靠的参数约束这个问题，因此是一个很有前途的技术，在宇宙学和天体物理学的其他应用。我们的ABC PMC方法的实现通过公共代码发布提供。
Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to the posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.