Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods

Maximum likelihood and Gaussian estimation of continuous time models in finance

Ministry of Education, Singapore under its Academic Research Funding Tier

Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance

Published in Handbook of financial time series, 2008, https://doi.org/10.1007/978-3-540-71297-8_22</p

Simulation-based Estimation Methods for Financial Time Series Models

Published in Handbook of computational finance, 2010, https://doi.org/10.1007/978-3-642-17254-0_15</p

Likelihood inference for Discretely Observed Non-linear Diffusions.

This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blcked Metropolis-Hastings algorithm, by introducing auxiliary points and by using the Euler-Maruyama discretisation scheme. Techniques for computing the likelihood function, the marginal likelihood and diagnostic measures (all based on the MCMC output) are presented

Likelihood inference for discretely observed non-linear diffusions

This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the latent data and the model parameters. Techniques for computing the likelihood function, the marginal likelihood, and diagnostic measures (all based on the MCMC output) are developed. Examples using simulated and real data are presented and discussed in detail

On the specification of the drift and diffusion functions for continuous-time models of the spot interest rate

This paper explores the specification of drift and diffusion functions for continuous-time short-term interest rate models. Various forms for the drift and diffusion of 7-day Eurodollar rates are proposed and then estimated by discrete maximum-likelihood. The results suggest that a nonparametric specification of drift and volatility in terms of orthogonal polynomial expansions is effective in eliminating problems of parameter identification encountered previously. Some evidence is found to support the claim that the drift of the short term interest rate is nonlinear

Likelihood inference for discretely observed non-linear diffusions

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