  In microbial studies, samples are often treated under different experimental
conditions and then tested for microbial survival. A technique, dating back to
the 1880's, consists of diluting the samples several times and incubating each
dilution to verify the existence of microbial Colony Forming Units or CFU's,
seen by the naked eye. The main problem in the dilution series data analysis is
the uncertainty quantification of the simple point estimate of the original
number of CFU's in the sample (i.e., at dilution zero). Common approaches such
as log-normal or Poisson models do not seem to handle well extreme cases with
low or high counts, among other issues. We build a novel binomial model, based
on the actual design of the experimental procedure including the dilution
series. For repetitions we construct a hierarchical model for experimental
results from a single lab and in turn a higher hierarchy for inter-lab
analyses. Results seem promising, with a systematic treatment of all data
cases, including zeros, censored data, repetitions, intra and inter-laboratory
studies. Using a Bayesian approach, a robust and efficient MCMC method is used
to analyze several real data sets.
