87,027 research outputs found
Markov chain design problems / 474
Includes bibliographical references (p. 17)
Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
We construct a new framework for accelerating Markov chain Monte Carlo in
posterior sampling problems where standard methods are limited by the
computational cost of the likelihood, or of numerical models embedded therein.
Our approach introduces local approximations of these models into the
Metropolis-Hastings kernel, borrowing ideas from deterministic approximation
theory, optimization, and experimental design. Previous efforts at integrating
approximate models into inference typically sacrifice either the sampler's
exactness or efficiency; our work seeks to address these limitations by
exploiting useful convergence characteristics of local approximations. We prove
the ergodicity of our approximate Markov chain, showing that it samples
asymptotically from the \emph{exact} posterior distribution of interest. We
describe variations of the algorithm that employ either local polynomial
approximations or local Gaussian process regressors. Our theoretical results
reinforce the key observation underlying this paper: when the likelihood has
some \emph{local} regularity, the number of model evaluations per MCMC step can
be greatly reduced without biasing the Monte Carlo average. Numerical
experiments demonstrate multiple order-of-magnitude reductions in the number of
forward model evaluations used in representative ODE and PDE inference
problems, with both synthetic and real data.Comment: A major update of the theory and example
Fault accommodation controller under Markovian jump linear systems with asynchronous modes
We tackle the fault accommodation control (FAC) in the Markovian jump linear system (MJLS) framework for the discrete-time domain, under the assumption that it is not possible to access the Markov chain mode. This premise brings some challenges since the controllers are no longer allowed to depend on the Markov chain, meaning that there is an asynchronism between the system and the controller modes. To tackle this issue, a hidden Markov chain ((Formula presented.), (Formula presented.)) is used where θ(k) denotes the Markov chain mode, and (Formula presented.) denotes the estimated mode. The main novelty of this work is the design of H∞ and H2 FAC under the MJLS framework considering partial observation of the Markov chain. Both designs are obtained via bilinear matrix inequalities optimization problems, which are solved using coordinate descent algorithm. As secondary results, we present simulations using a two-degree of freedom serial flexible joint robot to illustrate the viability of the proposed approach
A Note on the Art of Network Design Problems
In this study, we describe some Network Design Problems (NDPs) as well as the network flowbased improvement algorithm for neighbourhood search defined by cycles. The main part of the study is structured around the formulation of the expected duration of stay in the educational system as a NDP. The fundamental matrix of the absorbing Markov chain is employed in computing the expected duration of each flow in the system. We shall illustrate the new graphtheoretic formulation for the educational system using datasets from a university setting. The paper concludes with suggestions for future directions of research.Keywords: absorbing Markov chain; educational system; graph theory; network design
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