  The forensic science community has increasingly sought quantitative methods
for conveying the weight of evidence. Experts from many forensic laboratories
summarize their findings in terms of a likelihood ratio. Several proponents of
this approach have argued that Bayesian reasoning proves it to be normative. We
find this likelihood ratio paradigm to be unsupported by arguments of Bayesian
decision theory, which applies only to personal decision making and not to the
transfer of information from an expert to a separate decision maker. We further
argue that decision theory does not exempt the presentation of a likelihood
ratio from uncertainty characterization, which is required to assess the
fitness for purpose of any transferred quantity. We propose the concept of a
lattice of assumptions leading to an uncertainty pyramid as a framework for
assessing the uncertainty in an evaluation of a likelihood ratio. We
demonstrate the use of these concepts with illustrative examples regarding the
refractive index of glass and automated comparison scores for fingerprints.
