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Quantifying how microbes grow is therefore fundamental to areas such as genetics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth behavior through a set of summarizing parameters. However, estimation of these parameters from data is confounded by random effects such as experimental variability, batch effects or differences in experimental material. A systematic statistical method to identify and correct for such confounding effects in population growth data is not currently available. Further, our previous work has demonstrated that parametric models are insufficient to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding effects on measured population growth.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008366","type":"journal-article","created":{"date-parts":[[2020,10,26]],"date-time":"2020-10-26T18:48:55Z","timestamp":1603738135000},"page":"e1008366","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Bayesian non-parametric mixed-effects model of microbial growth curves"],"prefix":"10.1371","volume":"16","author":[{"given":"Peter D.","family":"Tonner","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7489-8584","authenticated-orcid":true,"given":"Cynthia L.","family":"Darnell","sequence":"additional","affiliation":[]},{"given":"Francesca M. 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SciPy: Open source scientific tools for Python; 2001. Available from: http:\/\/www.scipy.org\/."},{"key":"pcbi.1008366.ref053","volume-title":"Gaussian Processes for Machine Learning","author":"CE Rasmussen","year":"2006"},{"issue":"1","key":"pcbi.1008366.ref054","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1214\/10-BA505","article-title":"Bayesian functional ANOVA modeling using Gaussian process prior distributions","volume":"5","author":"CG Kaufman","year":"2010","journal-title":"Bayesian Analysis"},{"issue":"1","key":"pcbi.1008366.ref055","first-page":"1","article-title":"Stan: A Probabilistic Programming Language","volume":"76","author":"B Carpenter","year":"2017","journal-title":"Journal of Statistical Software, Articles"},{"issue":"4","key":"pcbi.1008366.ref056","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1080\/10618600.1998.10474787","article-title":"General Methods for Monitoring Convergence of Iterative Simulations","volume":"7","author":"SP Brooks","year":"1998","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"6","key":"pcbi.1008366.ref057","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1128\/AEM.03280-13","article-title":"Model organisms retain an \u201cecological memory\u201d of complex ecologically relevant environmental variation","volume":"80","author":"KD Beer","year":"2014","journal-title":"Applied and Environmental Microbiology"},{"key":"pcbi.1008366.ref058","unstructured":"Ramsay J, Silverman BW. Functional Data Analysis (Springer Series in Statistics). Springer; 2005. Available from: https:\/\/www.amazon.com\/Functional-Data-Analysis-Springer-Statistics\/dp\/038740080X?SubscriptionId=AKIAIOBINVZYXZQZ2U3A&tag=chimbori05-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=038740080X."},{"issue":"1","key":"pcbi.1008366.ref059","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/009053604000001048","article-title":"Analysis of variance\u2014why it is more important than ever","volume":"33","author":"A Gelman","year":"2005","journal-title":"The Annals of Statistics"},{"key":"pcbi.1008366.ref060","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","volume-title":"Bayesian Data Analysis","author":"A Gelman","year":"2013","edition":"3"},{"key":"pcbi.1008366.ref061","unstructured":"Solak E, Murray-Smith R, Leithead WE, Leith DJ, Rasmussen CE. Derivative Observations in Gaussian Process Models of Dynamic Systems. In: Proceedings of the 15th International Conference on Neural Information Processing Systems. NIPS\u201902. Cambridge, MA, USA: MIT Press; 2002. p. 1057\u20131064. Available from: http:\/\/dl.acm.org\/citation.cfm?id=2968618.2968750."},{"issue":"4","key":"pcbi.1008366.ref062","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1093\/bfgp\/3.4.322","article-title":"The importance of experimental design in proteomic mass spectrometry experiments: some cautionary tales","volume":"3","author":"J Hu","year":"2005","journal-title":"Briefings in Functional Genomics & Proteomics"},{"issue":"5","key":"pcbi.1008366.ref063","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1002\/sim.7175","article-title":"A note on statistical repeatability and study design for high-throughput assays","volume":"36","author":"G Nicholson","year":"2017","journal-title":"Statistics in Medicine"},{"issue":"10","key":"pcbi.1008366.ref064","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1093\/bioinformatics\/btq118","article-title":"Supervised normalization of microarrays","volume":"26","author":"BH 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