Particle and microorganism enumeration data: enabling quantitative rigor and judicious interpretation.

Many of the methods routinely used to quantify microscopic discrete particles and microorganisms are based on enumeration, yet these methods are often known to yield highly variable results. This variability arises from sampling error and variations in analytical recovery (i.e., losses during sample processing and errors in counting), and leads to considerable uncertainty in particle concentration or log(10)-reduction estimates. Conventional statistical analysis techniques based on the t-distribution are often inappropriate, however, because the data must be corrected for mean analytical recovery and may not be normally distributed with equal variance. Furthermore, these statistical approaches do not include subjective knowledge about the stochastic processes involved in enumeration. Here we develop two probabilistic models to account for the random errors in enumeration data, with emphasis on sampling error assumptions, nonconstant analytical recovery, and discussion of counting errors. These models are implemented using Bayes' theorem to yield posterior distributions (by numerical integration or Gibbs sampling) that completely quantify the uncertainty in particle concentration or log(10)-reduction given the experimental data and parameters that describe variability in analytical recovery. The presented approach can easily be implemented to correctly and rigorously analyze single or replicate (bio)particle enumeration data.