  We investigate whether quantum history theories can be consistent with
Bayesian reasoning and whether such an analysis helps clarify the
interpretation of such theories. First, we summarise and extend recent work
categorising two different approaches to formalising multi-time measurements in
quantum theory. The standard approach consists of describing an ordered series
of measurements in terms of history propositions with non-additive
`probabilities'. The non-standard approach consists of defining multi-time
measurements to consist of sets of exclusive and exhaustive history
propositions and recovering the single-time exclusivity of results when
discussing single-time history propositions. We analyse whether such history
propositions can be consistent with Bayes' rule. We show that certain class of
histories are given a natural Bayesian interpretation, namely the linearly
positive histories originally introduced by Goldstein and Page. Thus we argue
that this gives a certain amount of interpretational clarity to the
non-standard approach. We also attempt a justification of our analysis using
Cox's axioms of probability theory.
