  An important objective in environmental risk assessment is estimation of
minimum exposure levels, called Benchmark Doses (BMDs) that induce a
pre-specified Benchmark Response (BMR) in a target population. Established
inferential approaches for BMD analysis typically involve one-sided,
frequentist confidence limits, leading in practice to what are called Benchmark
Dose Lower Limits (BMDLs). Appeal to Bayesian modeling and credible limits for
building BMDLs is far less developed, however. Indeed, for the few existing
forms of Bayesian BMDs, informative prior information is seldom incorporated.
We develop reparameterized quantal-response models that explicitly describe the
BMD as a target parameter. Our goal is to obtain an improved estimation and
calculation archetype for the BMD and for the BMDL, by employing quantifiable
prior belief to represent parameter uncertainty in the statistical model.
Implementation is facilitated via a Monte Carlo-based adaptive Metropolis (AM)
algorithm to approximate the posterior distribution. An example from
environmental carcinogenicity testing illustrates the calculations.
