Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology
Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology
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DOI：
10.1093/mnras/sty819
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发表时间：
2018-07-01
影响因子：
4.8
通讯作者：
Feeney, Stephen
中科院分区：
文献类型：
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作者：
Alsing, Justin;Wandelt, Benjamin;Feeney, Stephen
宇宙学中的许多统计模型可以向前模拟，但具有棘手的似然函数。无似然推理方法使我们能够仅使用前向模拟从这些模型中执行贝叶斯推理，而无需任何似然假设或近似。无似然推理通常涉及模拟模拟数据并与观察到的数据进行比较；数据空间中的这种比较受到维数灾难的影响，并且需要将数据压缩为少量的汇总统计数据以便于处理。在本文中，我们使用大规模渐近最优数据压缩将数据空间的维度减少到每个参数只有一个数字，为无似然推理的汇总统计选择提供了一个自然且最优的框架。其次，我们提出了密度估计似然推理（DELFI）的第一个宇宙学应用，它学习数据和参数联合分布的参数化模型，产生参数后验和模型证据。这种方法在概念上很简单，与传统的近似贝叶斯计算方法相比，需要更少的调整来进行无似然推理，并且可以通过少几个数量级的前向模拟来提供高保真后验。作为额外的好处，它可以同时进行参数推断和贝叶斯模型比较。作为一个简单的验证案例研究，我们在联合光曲线分析超新星数据的分析中展示了具有大量数据压缩的 DELFI。我们表明，高保真后验推理对于全面的宇宙学数据分析来说是可能的，只需类似于 10(4) 的模拟，并且具有进一步改进的巨大空间，证明了对大型复杂宇宙学数据集的无似然推理的可扩展性。
Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper, we use massive asymptotically optimal data compression to reduce the dimensionality of the data space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (DELFI), which learns a parametrized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate DELFI with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as similar to 10(4) simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological data sets.