We present a novel Bayesian inference tool that uses a neural network (NN) to parametrize efficient Markov Chain Monte Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of non-linear, invertible, and non-volume preserving flows. NNs are extremely expressive, and can transform complex targets to a simple latent representation. Efficient proposals can then be made in this space, and we demonstrate a high degree of mixing on several challenging distributions. Parameter space can naturally be split into a block diagonal speed hierarchy, allowing for fast exploration of subspaces where it is inexpensive to evaluate the likelihood. Using this method, we develop a nested MCMC sampler to perform Bayesian inference and model comparison, finding excellent performance on highly curved and multimodal analytic likelihoods. We also test it on Planck 2015 data, showing accurate parameter constraints, and calculate the evidence for simple one-parameter extensions to the standard cosmological model in ∼20D parameter space. Our method has wide applicability to a range of problems in astronomy and cosmology and is available for download from https://github.com/adammoss/nnest.

中文翻译：

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使用深度学习加速贝叶斯推理

我们提出了一种新颖的贝叶斯推理工具，它使用神经网络 (NN) 来参数化有效的马尔可夫链蒙特卡罗 (MCMC) 建议。目标分布首先通过一系列非线性、可逆和非体积保持流转换为对角线单位方差高斯分布。NN 极具表现力，可以将复杂的目标转换为简单的潜在表示。然后可以在这个空间中提出有效的建议，我们展示了几个具有挑战性的分布的高度混合。参数空间可以自然地分成块对角线速度层次结构，允许快速探索子空间，其中评估可能性的成本很低。使用这种方法，我们开发了一个嵌套的 MCMC 采样器来执行贝叶斯推理和模型比较，在高度弯曲和多模态分析似然上找到出色的表现。我们还在 Planck 2015 数据上对其进行了测试，显示了准确的参数约束，并计算了 ∼20D 参数空间中标准宇宙学模型的简单单参数扩展的证据。我们的方法对天文学和宇宙学中的一系列问题具有广泛的适用性，可从 https://github.com/adammoss/nnest 下载。