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Estimating Bayes factors via thermodynamic integration and population MCMC

By B. Calderhead and M. Girolami

Abstract

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. (C) 2009 Elsevier B.V. All rights reserve

Publisher: Elsevier
Year: 2009
OAI identifier: oai:eprints.gla.ac.uk:34589
Provided by: Enlighten

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Citations

  1. (2001). Annealed importance sampling.
  2. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap.
  3. (1991). Bayes factors for nonlinear hypotheses and likelihood distributions. doi
  4. (1995). Bayes factors. doi
  5. (2007). Bayesian inference for nonlinear multivariate diffusion models observed with error. doi
  6. (2008). Bayesian ranking of biochemical system models. doi
  7. (2007). Bayesian Statistics. doi
  8. (2006). Comparison of methodologies to assess the convergence of Markov Chain Monte Carlo methods. doi
  9. (2006). Computing Bayes factors using thermodynamic integration. doi
  10. (2007). Estimating the integrated likelihood via posterior simulation using the harmonic mean identity.
  11. (1992). Inference from iterative simulation using multiple sequences. doi
  12. (2008). Marginal likelihood estimation via power posteriors. doi
  13. (2002). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman and Hall/CRC. doi
  14. (2005). Modelling genetic networks with noisy and 31varied experimental data: the circadian clock in arabidopsis thaliana. doi
  15. (2005). Modelling genetic networks with noisy and varied experimental data: the circadian clock in arabidopsis thaliana. doi
  16. (2004). Monte Carlo Statistical Methods. doi
  17. (2007). On population-based simulation for static inference. doi
  18. (1965). Oscillatory behavior in enzymatic control processes. doi
  19. (2003). Population Markov Chain Monte Carlo.
  20. (2000). Population Monte Carlo algorithms. doi
  21. (2001). Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models. doi
  22. (2006). Sequential Monte Carlo samplers. doi
  23. (1998). Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. doi

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