Rejoinder on “Likelihood-based belief function: Justification and some extensions to low-quality data”

•The axiomatic justification of likelihood-based belief functions is discussed.•This solution is not claimed to be unique.•Bayesian analysis yields different results in the case of uncertain data.

This note is a rejoinder to comments by Dubois and Moral about my paper “Likelihood-based belief function: justification and some extensions to low-quality data” published in this issue. The main comments concern (1) the axiomatic justification for defining a consonant belief function in the parameter space from the likelihood function and (2) the Bayesian treatment of statistical inference from uncertain observations, when uncertainty is quantified by belief functions. Both issues are discussed in this note, in response to the discussants' comments.