Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In this work, we present hierarchical neural posterior estimation (HNPE), a novel method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. Our method extends recent developments in simulation-based inference (SBI) based on normalizing flows to Bayesian hierarchical models. We validate quantitatively our proposal on a motivating example amenable to analytical solutions and then apply it to invert a well known non-linear model from computational neuroscience, using both simulated and real EEG data.
翻译:根据实验性观测推断出基于实验性观测的随机模型的参数是科学方法的核心。一个特别具有挑战性的设置是当模型非常不确定时,即当不同的参数组产生相同的观测结果时。这在许多实际情况下发生,例如当推断无线电源的距离和功率(源近、弱、强? )时,或当估计电子生理实验的放大器增益和潜在大脑活动时。在这项工作中,我们提出了等级神经远视估计(HNPE),这是利用一组共享全球参数的辅助观测所传送的额外信息破除这种不确定性的一种新颖的方法。我们的方法扩展了基于对巴伊西亚等级模型流的正常化的模拟推论(SBI)的最新发展情况。我们用模拟和真实的EEG数据从计算性神经科学中将它应用于众所周知的非线性模型。我们用模拟和真实的模拟数据,从数量上验证了我们关于一个有利于分析解决办法的例子的建议。