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      Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

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          Abstract

          Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.

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          Most cited references 11

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          Population growth of human Y chromosomes: a study of Y chromosome microsatellites

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            Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation.

            The simulation of biochemical kinetic systems is a powerful approach that can be used for: (i) checking the consistency of a postulated model with a set of experimental measurements, (ii) answering 'what if?' questions and (iii) exploring possible behaviours of a model. Here we describe a generic approach to combine numerical optimization methods with biochemical kinetic simulations, which is suitable for use in the rational design of improved metabolic pathways with industrial significance (metabolic engineering) and for solving the inverse problem of metabolic pathways, i.e. the estimation of parameters from measured variables. We discuss the suitability of various optimization methods, focusing especially on their ability or otherwise to find global optima. We recommend that a suite of diverse optimization methods should be available in simulation software as no single one performs best for all problems. We describe how we have implemented such a simulation-optimization strategy in the biochemical kinetics simulator Gepasi and present examples of its application. The new version of Gepasi (3.20), incorporating the methodology described here, is available on the Internet at http://gepasi.dbs.aber.ac.uk/softw/Gepasi. html. prm@aber.ac.uk
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              Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example.

              The basic reproductive rate (R0) is a measure of the severity of an epidemic. On the basis of replicated Latin hypercube sampling, the authors performed an uncertainty and sensitivity analysis of the basic reproductive rate of tuberculosis (TB). The uncertainty analysis allowed for the derivation of a frequency distribution for R0 and the assessment of the relative contribution each of the three components of R0 made when TB epidemics first arose centuries ago. (The three components of R0 are associated with fast, slow, and relapse TB.) R0 estimates indicated the existence of fairly severe epidemics when TB epidemics first arose. The R0 for the susceptible persons who developed TB slowly (R0(slow)) contributed the most to the R0 estimates; however, the relative R0(slow) contribution decreased as the severity of TB epidemics increased. The sensitivity of the magnitude of R0 to the uncertainty in estimating values of each of the input parameters was assessed. These results indicated that five of the nine input parameters, because of their estimation uncertainty, were influential in determining the magnitude of R0. This uncertainty and sensitivity methodology provides results that can aid investigators in understanding the historical epidemiology of TB by quantifying the effect of the transmission processes involved. Additionally, this method can be applied to the R0 of any other infectious disease to estimate the probability of an epidemic outbreak.
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                Author and article information

                Journal
                13 January 2009
                Article
                10.1098/rsif.2008.0172
                0901.1925

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Journal of the Royal Society Interface, Volume 6, Number 31, 2009, pages 187-202
                26 pages, 9 figures
                stat.CO stat.ME

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