In microbial studies, samples are often treated under different experimental conditions and then tested for microbial survival. A technique, dating back to the 1880s, 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 laboratory and in turn a higher hierarchy for inter-laboratory 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.

中文翻译：

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稀释系列微生物数据的系统统计分析

在微生物研究中，样品通常在不同的实验条件下进行处理，然后测试微生物的存活率。一项可追溯到 1880 年代的技术包括将样品稀释数次并孵育每次稀释液，以验证肉眼可见的微生物菌落形成单位或 CFU 的存在。稀释系列数据分析中的主要问题是样品中 CFU 原始数量的简单点估计的不确定性量化（即，稀释为零）。对数正态模型或泊松模型等常见方法似乎不能很好地处理计数低或高的极端情况等问题。我们基于包括稀释系列在内的实验程序的实际设计，构建了一个新的二项式模型。对于重复，我们为来自单个实验室的实验结果构建了一个层次模型，进而为实验室间分析构建了一个更高的层次结构。结果似乎很有希望，系统处理所有数据案例，包括零、删失数据、重复、实验室内和实验室间研究。使用贝叶斯方法，使用稳健且高效的 MCMC 方法来分析多个真实数据集。