Uncertain Evidence in Probabilistic Models and Stochastic Simulators
This work addresses a methodological issue for researchers and practitioners in probabilistic modeling and Bayesian inference, but it is incremental as it revisits and compares existing methods.
The paper tackles the problem of Bayesian inference with uncertain evidence in probabilistic models, exploring interpretations like distributional evidence, Jeffrey's rule, and virtual evidence, and provides guidelines and experimental comparisons to illustrate the impact of different interpretations on inference results.
We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." 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 "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise 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 one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.