358 research outputs found
Bayesian and Markov chain Monte Carlo methods for identifying nonlinear systems in the presence of uncertainty
In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories
Wormhole Hamiltonian Monte Carlo
In machine learning and statistics, probabilistic inference involving
multimodal distributions is quite difficult. This is especially true in high
dimensional problems, where most existing algorithms cannot easily move from
one mode to another. To address this issue, we propose a novel Bayesian
inference approach based on Markov Chain Monte Carlo. Our method can
effectively sample from multimodal distributions, especially when the dimension
is high and the modes are isolated. To this end, it exploits and modifies the
Riemannian geometric properties of the target distribution to create
\emph{wormholes} connecting modes in order to facilitate moving between them.
Further, our proposed method uses the regeneration technique in order to adapt
the algorithm by identifying new modes and updating the network of wormholes
without affecting the stationary distribution. To find new modes, as opposed to
rediscovering those previously identified, we employ a novel mode searching
algorithm that explores a \emph{residual energy} function obtained by
subtracting an approximate Gaussian mixture density (based on previously
discovered modes) from the target density function
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