In this work, we present an extension of the forward-reverse representation introduced by Bayer and Schoenmakers (Annals of Applied Probability, 24(5):1994-2032, 2014) to the context of stochastic reaction networks (S...
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In this work, we present an extension of the forward-reverse representation introduced by Bayer and Schoenmakers (Annals of Applied Probability, 24(5):1994-2032, 2014) to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, that is, SRNs conditional on their values in the extremes of given time intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation;then, during phase II, we apply the montecarlo version of the expectation-maximizationalgorithm to the phase I output. By selecting a set of overdispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.
Human neurodevelopment is a highly regulated biological process. In this article, we study the dynamic changes of neurodevelopment through the analysis of human brain microarray data, sampled from 16 brain regions in ...
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Human neurodevelopment is a highly regulated biological process. In this article, we study the dynamic changes of neurodevelopment through the analysis of human brain microarray data, sampled from 16 brain regions in 15 time periods of neurodevelopment. We develop a two-step inferential procedure to identify expressed and unexpressed genes and to detect differentially expressed genes between adjacent time periods. Markov Random Field (MRF) models are used to efficiently utilize the information embedded in brain region similarity and temporal dependency in our approach. We develop and implement a montecarloexpectation-maximization (MCEM) algorithm to estimate the model parameters. Simulation studies suggest that our approach achieves lower misclassification error and potential gain in power compared with models not incorporating spatial similarity and temporal dependency.
Factor analysis is a powerful tool to identify the common characteristics among a set of variables that are measured on a continuous scale. In the context of factor analysis for non-continuous-type data, most applicat...
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Factor analysis is a powerful tool to identify the common characteristics among a set of variables that are measured on a continuous scale. In the context of factor analysis for non-continuous-type data, most applications are restricted to item response data only. We extend the factor model to accommodate ranked data. The monte carlo expectation-maximization algorithm is used for parameter estimation at which the E-step is implemented via the Gibbs sampler. An analysis based on both complete and incomplete ranked data (e.g. rank the top q out of k items) is considered. Estimation of the factor scores is also discussed. The method proposed is applied to analyse a set of incomplete ranked data that were obtained from a survey that was carried out in GuangZhou, a major city in mainland China, to investigate the factors affecting people's attitude towards choosing jobs.
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