Fitting distributions to microbial contamination data collected with an unequal probability sampling design
Article first published online: 12 OCT 2012
© 2012 No claim to US Government works
Journal of Applied Microbiology
Volume 114, Issue 1, pages 152–160, January 2013
How to Cite
Williams, M.S., Ebel, E.D. and Cao, Y. (2013), Fitting distributions to microbial contamination data collected with an unequal probability sampling design. Journal of Applied Microbiology, 114: 152–160. doi: 10.1111/jam.12019
- Issue published online: 12 DEC 2012
- Article first published online: 12 OCT 2012
- Accepted manuscript online: 17 SEP 2012 09:24PM EST
- Manuscript Accepted: 13 SEP 2012
- Manuscript Revised: 21 AUG 2012
- Manuscript Received: 21 MAY 2012
- maximum likelihood estimation;
- risk assessment;
- sample design
The fitting of statistical distributions to microbial sampling data is a common application in quantitative microbiology and risk assessment applications. An underlying assumption of most fitting techniques is that data are collected with simple random sampling, which is often times not the case. This study develops a weighted maximum likelihood estimation framework that is appropriate for microbiological samples that are collected with unequal probabilities of selection.
Methods and Results
A weighted maximum likelihood estimation framework is proposed for microbiological samples that are collected with unequal probabilities of selection. Two examples, based on the collection of food samples during processing, are provided to demonstrate the method and highlight the magnitude of biases in the maximum likelihood estimator when data are inappropriately treated as a simple random sample.
Failure to properly weight samples to account for how data are collected can introduce substantial biases into inferences drawn from the data.
Significance and Impact of the Study
The proposed methodology will reduce or eliminate an important source of bias in inferences drawn from the analysis of microbial data. This will also make comparisons between studies and the combination of results from different studies more reliable, which is important for risk assessment applications.