1,282 research outputs found

    Gibbs flow for approximate transport with applications to Bayesian computation

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    Let π0\pi_{0} and π1\pi_{1} be two distributions on the Borel space (Rd,B(Rd))(\mathbb{R}^{d},\mathcal{B}(\mathbb{R}^{d})). Any measurable function T:RdRdT:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d} such that Y=T(X)π1Y=T(X)\sim\pi_{1} if Xπ0X\sim\pi_{0} is called a transport map from π0\pi_{0} to π1\pi_{1}. For any π0\pi_{0} and π1\pi_{1}, if one could obtain an analytical expression for a transport map from π0\pi_{0} to π1\pi_{1}, then this could be straightforwardly applied to sample from any distribution. One would map draws from an easy-to-sample distribution π0\pi_{0} to the target distribution π1\pi_{1} using this transport map. Although it is usually impossible to obtain an explicit transport map for complex target distributions, we show here how to build a tractable approximation of a novel transport map. This is achieved by moving samples from π0\pi_{0} using an ordinary differential equation with a velocity field that depends on the full conditional distributions of the target. Even when this ordinary differential equation is time-discretized and the full conditional distributions are numerically approximated, the resulting distribution of mapped samples can be efficiently evaluated and used as a proposal within sequential Monte Carlo samplers. We demonstrate significant gains over state-of-the-art sequential Monte Carlo samplers at a fixed computational complexity on a variety of applications.Comment: Significantly revised with new methodology and numerical example

    Almost optimal adaptive LQ control: observed state case

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    In this paper we propose an almost optimal indirect adaptive controller for input/state dynamical systems. The control part of the adaptive scheme is based on a modified LQ control law: by adding a time varying gain to the certainty equivalent control law we avoid the conflict between identification and contro

    Energetics and switching of quasi-uniform states in small ferromagnetic particles

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    We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size

    Remarks on drift estimation for diffusion processes

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    In applications such as molecular dynamics it is of interest to fit Smoluchowski and Langevin equations to data. Practitioners often achieve this by a variety of seemingly ad hoc procedures such as fitting to the empirical measure generated by the data, and fitting to properties of auto-correlation functions. Statisticians, on the other hand, often use estimation procedures which fit diffusion processes to data by applying the maximum likelihood principle to the path-space density of the desired model equations, and through knowledge of the properties of quadratic variation. In this note we show that these procedures used by practitioners and statisticians to fit drift functions are, in fact, closely related and can be thought of as two alternative ways to regularize the (singular) likelihood function for the drift. We also present the results of numerical experiments which probe the relative efficacy of the two approaches to model identification and compare them with other methods such as the minimum distance estimator

    Climatic influence in NRM and 10 Be-derived geomagnetic paleointensity data

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    One can determine geomagnetic paleointensities from natural remanent magnetizations (NRM) and by inverting production rates of cosmogenic isotopes such as 10 Be and 14 C. Recently, two independently derived 200-kyr stacks [Y. Guyodo, J.-P. Valet, Relative variations in geomagnetic intensity from sedimentary records: the past 200,000 years, Earth Planet. Sci. Lett. 143 (1996) 2336; M. Frank, B. Schwarz, S. Baumann, P.W. Kubik, M. Suter, A. Mangini, A 200 kyr record of cosmogenic radionuclide production rate and geomagnetic field intensity from 10 Be in globally stacked deep-sea sediments, Earth Planet. Sci. Lett. 149 (1997) 121129] were compared and the good agreement was suggested to validate the use of sedimentary cores for studies. Both compilations use mainly the astronomically forced and climatically controlled oxygen isotope stratigraphy to date and synchronize the sedimentary records, while this very curve has several coherent features with the supposedly pure geomagnetic records. An NRM relative paleointensity record, which was included in the conventional paleointensity stack, shows correspondence with climatic features, which is explained by an inadequacy in the normalization technique. Therefore, it is possible that the extraction of the pure paleointensity signal from marine sediments has not always been accomplished. Ó 1999 Elsevier Science B.V. All rights reserved
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