Missing data in amortized simulation-based neural posterior estimation.

Amortized simulation-based neural posterior estimation provides a novel machine learning based approach for solving parameter estimation problems. It has been shown to be computationally efficient and able to handle complex models and data sets. Yet, the available approach cannot handle the in experimental studies ubiquitous case of missing data, and might provide incorrect posterior estimates. In this work, we discuss various ways of encoding missing data and integrate them into the training and inference process. We implement the approaches in the BayesFlow methodology, an amortized estimation framework based on invertible neural networks, and evaluate their performance on multiple test problems. We find that an approach in which the data vector is augmented with binary indicators of presence or absence of values performs the most robustly. Indeed, it improved the performance also for the simpler problem of data sets with variable length. Accordingly, we demonstrate that amortized simulation-based inference approaches are applicable even with missing data, and we provide a guideline for their handling, which is relevant for a broad spectrum of applications. Author summary: In biomedical research, mechanistic models describe dynamic processes, yet inferring their underlying parameters can often be challenging. Bayesian statistics provides an established framework for this by integrating prior knowledge with observed data, and naturally enables uncertainty quantification as a distribution of parameter values is returned. However, classical case-based methods for Bayesian inference can be computationally expensive, particularly when the same model needs to be fitted to different data sets. Recently, deep-learning-based approaches have been developed to streamline the inference procedure, allowing the upfront training cost to amortize when applied to multiple data sets. In this manuscript, we explore approaches to extend the setup to data sets with missing data. In summary, an encoding scheme which exploits data augmentation with binary indicators of presence or absence performs the most robustly across different test problems. [ABSTRACT FROM AUTHOR]