Many complicated Bayesian posteriors are difficult to approximate by either sampling or optimisation methods. Therefore we propose a novel approach combining features of both. We use a flexible parameterised family of densities, such as a normalising flow. Given a density from this family approximating the posterior, we use importance sampling to produce a weighted sample from a more accurate posterior approximation. This sample is then used in optimisation to update the parameters of the approximate density, which we view as distilling the importance sampling results. We iterate these steps and gradually improve the quality of the posterior approximation. We illustrate our method in two challenging examples: a queueing model and a stochastic differential equation model.
翻译:许多复杂的Bayesian后子星很难通过抽样或优化方法加以估计。 因此, 我们提出一种将两者的特征结合起来的新办法。 我们使用一个灵活的密度参数组合, 如正常化流程。 由于这个家族的密度接近后子星, 我们使用重要抽样从更精确的后子近似中生成一个加权样本。 然后, 这个样本被优化地用于更新大约密度的参数, 我们认为这是提取重要取样结果的结果。 我们对这些步骤进行循环, 并逐渐提高后子近似的质量。 我们用两个具有挑战性的例子来说明我们的方法: 排队模型和随机偏差公式模型。