This thesis consists of four original pieces of work contained in chapters 2,3,4 and 5. These cover four topics within the area of statistical methods for parameter estimation of biochemical kinetic models. Emphasis is put on integrating single-cell reporter gene data with stochastic dynamic models. \ud Chapter 2 introduces a modelling framework based on stochastic and ordinary differential equations that addresses the problem of reconstructing transcription time course profiles and associated degradation rates from fluorescent and luminescent reporter genes. We present three case studies where the methodology is used to reconstruct unobserved transcription profiles and to estimate associated degradation rates. \ud In Chapter 3 we use the linear noise approximation to model biochemical reactions through a stochastic dynamic model and derive an explicit formula for the likelihood function which allows for computationally efficient parameter estimation. The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly techniques of data augmentation are not necessary. \ud In Chapter 4 we present an inference framework for interpretation of fluorescent reporter gene data. The method takes into account stochastic variability in a fluorescent signal resulting from intrinsic noise of gene expression, extrinsic noise and kinetics of fluorescent protein maturation. \ud Chapter 5 presents a Bayesian hierarchical model, that allows us to infer distributions of fluorescent reporter degradation rates. \ud All methods are embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo
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