Estimating bacterial density from tube dilution data by a Bayesian method

We have developed a statistical computer program based on a Bayesian approach to estimate bacterial density from tube dilution data. The program calculates an expectation, a mode (equivalent to the traditional most probable number (MPN)) and a median as point estimates of the bacterial density. The Bayesian analysis provides a probability density function which reflects the knowledge accumulated about the bacterial density by observing the data. Its expectation is a summery value that incorporates the shape and skewness of the distribution. On the other hand, the MPN (mode) only uses the single most likely value and ignores other values that are consistent with the data. As a result the MPN consistently underestimates the bacterial density and is likely to produce large errors. Thus we recommend the use of the expectation as an estimator for most problems. The theoretical basis of the Bayesian approach and its application to Salmonella data is discussed. Tables of results for different combinations of tube dilutions are also presented.