论文标题
贝叶斯普通微分方程模型的可靠和有效推断的重要性抽样方法
An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models
论文作者
论文摘要
统计模型可能涉及隐式定义的数量，例如非线性普通微分方程（ODE）的解决方案，不可避免地需要在数值上近似以评估该模型。近似误差固有地偏向统计推断结果，但是这种偏差的量通常未知，并且在贝叶斯参数推断中通常被忽略。我们提出了一种使用Markov Chain Monte Carlo方法进行推理时，提出了一种计算有效的方法，用于验证此类模型后验推断的可靠性。我们使用模拟和真实数据以及不同的ODE求解器验证实验中工作流程的效率和可靠性。我们重点介绍了使用常用的自适应ODE求解器引起的问题，并提出了强大而有效的替代方案，这些替代方案伴随着我们的工作流程，可以在不失去推论的可靠性的情况下使用。
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation error inherently biases statistical inference results, but the amount of this bias is generally unknown and often ignored in Bayesian parameter inference. We propose a computationally efficient method for verifying the reliability of posterior inference for such models, when the inference is performed using Markov chain Monte Carlo methods. We validate the efficiency and reliability of our workflow in experiments using simulated and real data, and different ODE solvers. We highlight problems that arise with commonly used adaptive ODE solvers, and propose robust and effective alternatives which, accompanied by our workflow, can now be taken into use without losing reliability of the inferences.
