Statistics and Computing
On population-based simulation for static inference
Statistics and Computing
Bayesian inference for nonlinear multivariate diffusion models observed with error
Computational Statistics & Data Analysis
Bayesian ranking of biochemical system models
Bioinformatics
Comparison of methodologies to assess the convergence of Markov chain Monte Carlo methods
Computational Statistics & Data Analysis
Monte Carlo Statistical Methods
Monte Carlo Statistical Methods
Statistics and Computing
Smooth functional tempering for nonlinear differential equation models
Statistics and Computing
Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm
Computational Statistics & Data Analysis
Classification of molecular sequence data using Bayesian phylogenetic mixture models
Computational Statistics & Data Analysis
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A Bayesian approach to model comparison based on the integrated or marginal likelihood is considered, and applications to linear regression models and nonlinear ordinary differential equation (ODE) models are used as the setting in which to elucidate and further develop existing statistical methodology. The focus is on two methods of marginal likelihood estimation. First, a statistical failure of the widely employed Posterior Harmonic Mean estimator is highlighted. It is demonstrated that there is a systematic bias capable of significantly skewing Bayes factor estimates, which has not previously been highlighted in the literature. Second, a detailed study of the recently proposed Thermodynamic Integral estimator is presented, which characterises the error associated with its discrete form. An experimental study using analytically tractable linear regression models highlights substantial differences with recently published results regarding optimal discretisation. Finally, with the insights gained, it is demonstrated how Population MCMC and thermodynamic integration methods may be elegantly combined to estimate Bayes factors accurately enough to discriminate between nonlinear models based on systems of ODEs, which has important application in describing the behaviour of complex processes arising in a wide variety of research areas, such as Systems Biology, Computational Ecology and Chemical Engineering.