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28
On Bayesian Inference for Stochastic Kinetic Models Using Diffusion Approximations
, 2004
"... This paper is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a di#usion approximation (or stochastic di#erential equation approach) where a white noise t ..."
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Cited by 25 (7 self)
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This paper is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a di#usion approximation (or stochastic di#erential equation approach) where a white noise term models stochastic behaviour and the model is identified using equispaced time course data. The estimation framework involves the introduction of m1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters
Bayesian sequential inference for stochastic kinetic biochemical network models J Comput Biol
, 2006
"... As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The ..."
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Cited by 22 (6 self)
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As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The underlying model is replaced by a diffusion approximation where a noise term represents intrinsic stochastic behavior and the model is identified using discretetime (and often incomplete) data that is subject to measurement error. Sequential MCMC methods are then used to sample the model parameters online in several datapoor contexts. The methodology is illustrated by applying it to the estimation of parameters in a simple prokaryotic autoregulatory gene network.
Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC
"... We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing ..."
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Cited by 14 (2 self)
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We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forwardbackward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forwardbackward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discretestate continuoustime Markov chain; inferring structure in population genetics; and segmenting genetic divergence data.
Time series analysis via mechanistic models. In review; prepublished at arxiv.org/abs/0802.0021
, 2008
"... The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consi ..."
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Cited by 13 (5 self)
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The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plugandplay property. Our work builds on recently developed plugandplay inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A
Variational inference for Markov jump processes
 In Advances in Neural Information Processing Systems 20
, 2007
"... Markov jump processes play an important role in a large number of application domains. However, realistic systems are analytically intractable and they have traditionally been analysed using simulation based techniques, which do not provide a framework for statistical inference. We propose a mean fi ..."
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Cited by 7 (1 self)
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Markov jump processes play an important role in a large number of application domains. However, realistic systems are analytically intractable and they have traditionally been analysed using simulation based techniques, which do not provide a framework for statistical inference. We propose a mean field approximation to perform posterior inference and parameter estimation. The approximation allows a practical solution to the inference problem, while still retaining a good degree of accuracy. We illustrate our approach on two biologically motivated systems.
Linking systems biology models to data: a stochastic kinetic model of p53 oscillations
, 2009
"... This chapter considers the assessment and refinement of a dynamic stochastic process model of the cellular response to DNA damage. The proposed model is a complex nonlinear continuous time latent stochastic process. It is compared to time course data on the levels of two key proteins involved in thi ..."
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Cited by 6 (2 self)
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This chapter considers the assessment and refinement of a dynamic stochastic process model of the cellular response to DNA damage. The proposed model is a complex nonlinear continuous time latent stochastic process. It is compared to time course data on the levels of two key proteins involved in this response, captured at the level of individual cells in a human cancer cell line. The primary goal of this study is to “calibrate ” the model by finding parameters of the model (kinetic rate constants) that are most consistent with the experimental data. Significant amounts of prior information are available for the model parameters. It is therefore most natural to consider a Bayesian analysis of the problem, using sophisticated MCMC methods to overcome the formidable computational challenges.
Mjolsness E: Towards the inference of stochastic biochemical network and parameterized grammar models. Learning and Inference
 in Computational Systems Biology MIT PressLawrence ND, Girolami M, Rattray M, Sanguinetti G 2009
"... Deterministic dynamical systems are used extensively for modeling in biological applications. Unfortunately, such models cannot take into account much of the stochastic behavior that arises in biological systems. Stochastic process models can capture the variance and higher moments that exist in noi ..."
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Cited by 4 (2 self)
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Deterministic dynamical systems are used extensively for modeling in biological applications. Unfortunately, such models cannot take into account much of the stochastic behavior that arises in biological systems. Stochastic process models can capture the variance and higher moments that exist in noisy real data. But the use of stochastic process models is limited because of the formidable task of inferring the model parameters ’ values from observations. In this chapter we discuss a parameter inference scheme for a family of stochastic processes that can be defined by generalized reactions or rewrite rules as they occur within the Stochastic Parameterized Grammars (SPGs) modeling framework. The chapter is organized as follows. Section 1 provides an overview of the related work on optimization techniques for both deterministic continuous models and stochastic processes. In Section 2 we introduce the SPG modeling framework and derive a sampling scheme for SPG models. The parameter inference problem is defined in Section 3. We describe the general MetropolisHastings algorithm in section 3.1, and demonstrate how to apply it to SPG models in 3.2. Section 4 presents the results for optimization in a stochastic model of chemical reactions. Possible extensions and comparison to related algorithms is discussed in Section 5. 1 1
CaliBayes and BASIS: integrated tools for the calibration, simulation and storage of biological simulation models
"... Dynamic simulation modelling of complex biological processes forms the backbone of systems biology. Discrete stochastic models are particularly appropriate for describing subcellular molecular interactions, especially when critical molecular species are thought to be present at low copynumbers. Fo ..."
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Cited by 2 (1 self)
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Dynamic simulation modelling of complex biological processes forms the backbone of systems biology. Discrete stochastic models are particularly appropriate for describing subcellular molecular interactions, especially when critical molecular species are thought to be present at low copynumbers. For example, these stochastic effects play an important role in models of human ageing, where ageing results from the longterm accumulation of random damage at various biological scales. Unfortunately, realistic stochastic simulation of discrete biological processes is highly computationally intensive, requiring specialist hardware, and can benefit greatly from parallel and distributed approaches to computation and analysis. For these reasons, we have developed the BASIS system for the simulation and storage of stochastic SBML models together with associated simulation results. This system is exposed as a set of web services to allow users to incorporate its simulation tools into their workflows. Parameter inference for stochastic models is also difficult and computationally expensive. The CaliBayes system provides a set of web services (together with an R package for consuming these and formatting data) which addresses this problem for SBML models. It uses a sequential Bayesian MCMC method which is powerful and flexible, providing very rich information. However this approach is exceptionally computationally intensive and requires the use of a carefully designed architecture. Again, these tools are exposed as web services to allow users to take advantage of this system. In this paper we describe these two systems and demonstrate their integrated use with an example workflow to estimate the parameters of a simple model of S. Cerevisiae growth on agar plates.
Markov chain Monte Carlo algorithms for SDE parameter estimation
, 2008
"... This chapter considers stochastic differential equations for Systems Biology models derived from the Chemical Langevin Equation (CLE). After outlining the derivation of such models, Bayesian inference for the parameters is considered, based on stateoftheart Markov chain Monte Carlo algorithms. St ..."
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Cited by 1 (0 self)
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This chapter considers stochastic differential equations for Systems Biology models derived from the Chemical Langevin Equation (CLE). After outlining the derivation of such models, Bayesian inference for the parameters is considered, based on stateoftheart Markov chain Monte Carlo algorithms. Starting with a basic scheme for models observed perfectly, but discretely in time, problems with standard schemes and their solutions are discussed. Extensions of these schemes to partial observation and observations subject to measurement error are also considered. Finally, the techniques are demonstrated in the context of a simple stochastic kinetic model of a genetic regulatory network. 1