Uncertain Evidence in Probabilistic Models and Stochastic Simulators

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as `uncertain evidence'. In many real-world scenarios, such uncertainty stems from measurement errors associated with observable quantities in probabilistic models. We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method `stochastic evidence' as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise concrete guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which we compare inference results associated with each interpretation.