  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.
