Likelihood-free inference involves inferring parameter values given observed data and a simulator model. The simulator is computer code which takes parameters, performs stochastic calculations, and outputs simulated data. In this work, we view the simulator as a function whose inputs are (1) the parameters and (2) a vector of pseudo-random draws. We attempt to infer all these inputs conditional on the observations. This is challenging as the resulting posterior can be high dimensional and involve strong dependence. We approximate the posterior using normalizing flows, a flexible parametric family of densities. Training data is generated by likelihood-free importance sampling with a large bandwidth value epsilon, which makes the target similar to the prior. The training data is "distilled" by using it to train an updated normalizing flow. The process is iterated, using the updated flow as the importance sampling proposal, and slowly reducing epsilon so the target becomes closer to the posterior. Unlike most other likelihood-free methods, we avoid the need to reduce data to low dimensional summary statistics, and hence can achieve more accurate results. We illustrate our method in two challenging examples, on queuing and epidemiology.

翻译：无似然推断涉及在给定观测数据和模拟器模型时推断参数值。模拟器是一种计算机代码，它接受参数、执行随机计算并输出模拟数据。在本研究中，我们将模拟器视为一个函数，其输入包括：(1) 参数和 (2) 一组伪随机数向量。我们试图在观测数据条件下推断所有这些输入。这一过程具有挑战性，因为所得后验分布可能是高维的且存在强依赖性。我们使用归一化流（一种灵活的密度参数族）来近似后验分布。训练数据通过无似然重要性采样生成，并采用较大的带宽值ε，使目标分布接近于先验分布。通过利用该训练数据训练更新后的归一化流，实现了数据的“精简”。这一过程迭代进行：将更新后的流作为重要性采样的提议分布，并逐步减小ε，使目标分布逐渐接近后验分布。与大多数其他无似然方法不同，我们避免了将数据降维至低维汇总统计量的需求，从而能够获得更精确的结果。我们通过两个具有挑战性的例子（排队论和流行病学）展示了该方法的应用。