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Title: A stochastic model for multiple bacteria growth curves based on the random telegraph process Authors:  Michael Wiper - Universidad Carlos III de Madrid (Spain) [presenting]
Ana Paula Palacios - Greenwich University (United Kingdom)
J Miguel Marin - University Carlos III (Spain)
Abstract: A new, stochastic model for growth curves is developed. This model is based on a time-stretched, integrated stochastic process. By design, the mean curve (assuming equilibrium) is a standard growth curve model. The underlying process is a Markov process with two states. When the associated rates are equal, the process is symmetric around the mean, in the sense that the expected skewness about the mean at any time point is zero. When the rates are different, then the process is asymmetric. As the likelihood function for this process cannot be derived, Maximum likelihood estimation cannot be used for inference purposes. Therefore, assuming a parametric mean growth curve, given a sample of growth curve data, least squares are used to estimate the curve. Then, the rates are estimated via the method of moments or approximate Bayesian computation. Furthermore, we show that we can decide whether to use the symmetric or asymmetric model using a standard test for asymmetry at a carefully chosen time point. The model is illustrated using both simulated data and a real data set of listeria growth curves.