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Variational Methods (variational + methods)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

On the adequacy of variational lower bound functions for likelihood-based inference in Markovian models with missing values

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2002
Peter Hall
Summary. Variational methods have been proposed for obtaining deterministic lower bounds for log-likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for the simple example of a first-order autoregressive model with missing values, that the lower bound surface can be very similar in shape to the true log-likelihood in non-asymptotic situations. [source]

Dynamic and generalized Wentzell node conditions for network equations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2007
Delio Mugnolo
Abstract Motivated by a neurobiological problem, we discuss a class of diffusion problems on a network. The celebrated Rall lumped soma model for the spread of electrical potential in a dendritical tree prescribes that the common cable equation must be coupled with particular dynamic conditions in some nodes (the cell bodies, or somata). We discuss the extension of this model to the case of a whole network of neurons, where the ramification nodes can be either active (with excitatory time-dependent boundary conditions) or passive (where no dynamics take place, i.e. only Kirchhoff laws are imposed). While well-posedness of the system has already been obtained in previous works, using abstract tools based on variational methods and semigroup theory we are able to prove several qualitative properties, including asymptotic behaviour, regularity of solutions, and monotonicity of the semigroups in dependence on the physical coefficients. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On a semilinear elliptic equation with singular term and Hardy,Sobolev critical growth

MATHEMATISCHE NACHRICHTEN, Issue 8 2007
Jianqing ChenArticle first published online: 8 MAY 200
Abstract In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with Hardy,Sobolev critical growth and singular term by using variational methods. The result obtained here, even in a particular case, relates with a partial (positive) answer to an open problem proposed in: A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations 177, 494,522 (2001). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Ensemble data assimilation with the CNMCA regional forecasting system

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 646 2010
Massimo Bonavita
Abstract The Ensemble Kalman Filter (EnKF) is likely to become a viable alternative to variational methods for the next generation of meteorological and oceanographic data assimilation systems. In this work we present results from real-data assimilation experiments using the CNMCA regional numerical weather prediction (NWP) forecasting system and compare them to the currently operational variational-based analysis. The set of observations used is the same as the one ingested in the operational data stream, with the exception of satellite radiances and scatterometer winds. Results show that the EnKF-based assimilation cycle is capable of producing analyses and forecasts of consistently superior skill in the root mean square error metric than CNMCA operational 3D-Var. One of the most important issues in EnKF implementations lies in the filter tendency to become underdispersive for practical ensemble sizes. To combat this problem a number of different parametrizations of the model error unaccounted for in the assimilation cycle have been proposed. In the CNMCA system a combination of adaptive multiplicative and additive background covariance inflations has been found to give adequate results and to be capable of avoiding filter divergence in extended assimilation trials. The additive component of the covariance inflation has been implemented through the use of scaled forecast differences. Following suggestions that ensemble square-root filters can violate the gaussianity assumption when used with nonlinear prognostic models, the statistical distribution of the forecast and analysis ensembles has been studied. No sign of the ensemble collapsing onto one or a few model states has been found, and the forecast and analysis ensembles appear to stay remarkably close to the assumed probability distribution functions. Copyright © 2010 Royal Meteorological Society [source]