Hello,
I am developing a model of the MPN index of faecal coliform that will be structured as generalized
linear mixed model.
The Most Probable Number (MPN) method involves treating water samples with an activating agent in
a series of replicate test tubes at different dilutions. Each test tube (per dilution) results in
either a positive or negative indication of faecal coliform. Typically, MPN is computed as the MLE
of the number of positive tubes X (per dilution) in a Binomial distribution with parameters: p =
1- prob of no growth; and n=number of tubes per dilution. This appraoch can be recognized as a
Poisson-Binomial mixture. The MLE and thus, MPN, is the mode of this (skewed) distribution.
I am interested in computing this model in a Bayesian approach and using the MPN (mode of the
posterior distribution) as the dependent variable in a generalized linear mixed model. I would
like to do this mostly because I am interested in internalizing the variability (from the
Poisson-Binomial distribution) around the MPN into the linear model.
(I suppose my first question is: does this make sense? And if so...)
I understand that I can compute the mode by taking simulations (from CODA) and generating the
kernel density.
Unless there is an easier way to obtain the mode, my question is how should I think about taking
this MPN estimate and its density back into WinBugs.
Best regards,
Chris Behr
Principal Analyst
eDesign Dynamics
(
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