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Bayesian State-Space Modelling on High-Performance Hardware Using LibBi

Lawrence M. Murray
CSIRO Mathematics, Informatics and Statistics
arXiv:1306.3277 [stat.CO], (14 Jun 2013)
@ARTICLE{2013arXiv1306.3277M,

   author={Murray}, L.~M.},

   title={"{Bayesian State-Space Modelling on High-Performance Hardware Using LibBi}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1306.3277},

   primaryClass={"stat.CO"},

   keywords={Statistics – Computation},

   year={2013},

   month={jun},

   adsurl={http://adsabs.harvard.edu/abs/2013arXiv1306.3277M},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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LibBi is a software package for state-space modelling and Bayesian inference on modern computer hardware, including multi-core central processing units (CPUs), many-core graphics processing units (GPUs) and distributed-memory clusters of such devices. The software parses a domain-specific language for model specification, then optimises, generates, compiles and runs code for the given model, inference method and hardware platform. In presenting the software, this work serves as an introduction to state-space models and the specialised methods developed for Bayesian inference with them. The focus is on sequential Monte Carlo (SMC) methods such as the particle filter for state estimation, and the particle Markov chain Monte Carlo (PMCMC) and SMC^2 methods for parameter estimation. All are well-suited to current computer hardware. Two examples are given and developed throughout, one a linear three-element windkessel model of the human arterial system, the other a nonlinear Lorenz ’96 model. These are specified in the prescribed modelling language, and LibBi demonstrated by performing inference with them. Empirical results are presented, including a performance comparison of the software with different hardware configurations.
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