Simulation based inference (SBI) methods enable the estimation of posterior distributions when the likelihood function is intractable, but where model simulation is feasible. Popular neural approaches to SBI are the neural posterior estimator (NPE) and its sequential version (SNPE). These methods can outperform statistical SBI approaches such as approximate Bayesian computation (ABC), particularly for relatively small numbers of model simulations. However, we show in this paper that the NPE methods are not guaranteed to be highly accurate, even on problems with low dimension. In such settings the posterior cannot be accurately trained over the prior predictive space, and even the sequential extension remains sub-optimal. To overcome this, we propose preconditioned NPE (PNPE) and its sequential version (PSNPE), which uses a short run of ABC to effectively eliminate regions of parameter space that produce large discrepancy between simulations and data and allow the posterior emulator to be more accurately trained. We present comprehensive empirical evidence that this melding of neural and statistical SBI methods improves performance over a range of examples, including a motivating example involving a complex agent-based model applied to real tumour growth data.

翻译：基于模拟的推断（SBI）方法能够在似然函数难以计算但模型模拟可行的情况下估计后验分布。流行的神经SBI方法包括神经后验估计器（NPE）及其序贯版本（SNPE）。这些方法在模型模拟次数相对较少时，可优于近似贝叶斯计算（ABC）等统计SBI方法。然而，本文表明NPE方法即使在低维问题上也无法保证高精度。在此类场景中，后验无法在先验预测空间上被准确训练，即使序贯扩展方法仍存在次优性。为解决该问题，我们提出预条件化神经后验估计（PNPE）及其序贯版本（PSNPE），该方法通过短程ABC运行有效消除参数空间中模拟与数据产生较大差异的区域，从而使后验模拟器得到更精确的训练。我们通过全面的实证证据表明，这种神经与统计SBI方法的融合在多个实例中提升了性能，其中包括一个应用于真实肿瘤生长数据的复杂基于主体模型的激励性案例。