Perturbation-based inference for diffusion processes: Obtaining effective models from multiscale data
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We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or NURBS mapping which we assume to be regular. The numerical solution of the PDE is computed by ...
We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...
Bilinear models of count data with Poisson distribution are popular in applications such as matrix factorization for recommendation systems, modeling of receptive fields of sensory neurons, and modeling of neural-spike trains. Bayesian inference in such mo ...
Adaptive networks consist of a collection of nodes that interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the performance of two di ...
In this report, we investigate mathematical algorithms for image reconstruction in the context of positron emission tomography (a medical diagnosis technique). We first take inspiration from the physics of PET to design a mathematical model tailored to the ...
We consider the problem of estimation in a partially observed discrete-time Galton-Watson branching process, focusing on the first two moments of the offspring distribution. Our study is motivated by modelling the counts of new cases at the onset of a stoc ...
We consider the problem of estimation in a partially observed discrete-time Galton-Watson branching process, focusing on the first two moments of the offspring distribution. Our study is motivated by modelling the counts of new cases at the onset of a stoc ...
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...
In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...
Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although some frequentist properties of the maximum composite likelihood estimator are akin to those of the maximu ...
Academia Sinica, Institute of Statistical Science2012