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Open AccessProceedings

TI-Stan: Adaptively Annealed Thermodynamic Integration with HMC

Department of Electrical Engineering, University of Mississippi, University, MS 38677, USA
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Presented at the 39th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany, 30 June–5 July 2019.
These authors contributed equally to this work.
Proceedings 2019, 33(1), 9; https://doi.org/10.3390/proceedings2019033009
Published: 22 November 2019
We present a novel implementation of the adaptively annealed thermodynamic integration technique using Hamiltonian Monte Carlo (HMC). Thermodynamic integration with importance sampling and adaptive annealing is an especially useful method for estimating model evidence for problems that use physics-based mathematical models. Because it is based on importance sampling, this method requires an efficient way to refresh the ensemble of samples. Existing successful implementations use binary slice sampling on the Hilbert curve to accomplish this task. This implementation works well if the model has few parameters or if it can be broken into separate parts with identical parameter priors that can be refreshed separately. However, for models that are not separable and have many parameters, a different method for refreshing the samples is needed. HMC, in the form of the MC-Stan package, is effective for jointly refreshing the ensemble under a high-dimensional model. MC-Stan uses automatic differentiation to compute the gradients of the likelihood that HMC requires in about the same amount of time as it computes the likelihood function itself, easing the programming burden compared to implementations of HMC that require explicitly specified gradient functions. We present a description of the overall TI-Stan procedure and results for representative example problems.
Keywords: model comparison; MCMC; thermodynamic integration; HMC model comparison; MCMC; thermodynamic integration; HMC
MDPI and ACS Style

Henderson, R.W.; Goggans, P.M. TI-Stan: Adaptively Annealed Thermodynamic Integration with HMC . Proceedings 2019, 33, 9.

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