1,665 research outputs found

    A class of fast exact Bayesian filters in dynamical models with jumps

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    In this paper, we focus on the statistical filtering problem in dynamical models with jumps. When a particular application relies on physical properties which are modeled by linear and Gaussian probability density functions with jumps, an usualmethod consists in approximating the optimal Bayesian estimate (in the sense of the Minimum Mean Square Error (MMSE)) in a linear and Gaussian Jump Markov State Space System (JMSS). Practical solutions include algorithms based on numerical approximations or based on Sequential Monte Carlo (SMC) methods. In this paper, we propose a class of alternative methods which consists in building statistical models which share the same physical properties of interest but in which the computation of the optimal MMSE estimate can be done at a computational cost which is linear in the number of observations.Comment: 21 pages, 7 figure

    Approximation of epidemic models by diffusion processes and their statistical inference

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    Multidimensional continuous-time Markov jump processes (Z(t))(Z(t)) on Zp\mathbb{Z}^p form a usual set-up for modeling SIRSIR-like epidemics. However, when facing incomplete epidemic data, inference based on (Z(t))(Z(t)) is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating (Z(t))(Z(t)). First, \previous results on the approximation of density-dependent SIRSIR-like models by diffusion processes with small diffusion coefficient 1N\frac{1}{\sqrt{N}}, where NN is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number nn of observations, which corresponds to the epidemic context, and for N→∞N\rightarrow \infty. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as R0R_0 (the basic reproduction number), NN, nn are investigated on simulations. Two models, SIRSIR and SIRSSIRS, corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.Comment: 30 pages, 10 figure

    Efficient statistical inference for stochastic reaction processes

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    We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we derive an efficient approximation for this problem. We demonstrate the validity of our approach on model systems and generalize our method to the case when some state variables are not observed.Comment: 4 pages, 2 figures, 2 tables; typos corrected, remark about Kalman smoother adde

    Fault accommodation controller under Markovian jump linear systems with asynchronous modes

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    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
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