Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Richard Nickl"'
Publikováno v:
Oberwolfach Reports. 18:1191-1208
Publikováno v:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 381 (2247)
We exhibit examples of high-dimensional unimodal posterior distributions arising in nonlinear regression models with Gaussian process priors for which Markov chain Monte Carlo (MCMC) methods can take an exponential run-time to enter the regions where
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Publikováno v:
Communications on Pure and Applied Mathematics
For $M$ a simple surface, the non-linear statistical inverse problem of recovering a matrix field $\Phi: M \to \mathfrak{so}(n)$ from discrete, noisy measurements of the $SO(n)$-valued scattering data $C_\Phi$ of a solution of a matrix ODE is conside
Autor:
Richard Nickl
Publikováno v:
Journal of the European Mathematical Society. 22:2697-2750
Publikováno v:
SIAM/ASA Journal on Uncertainty Quantification. 8:374-413
We consider PDE constrained nonparametric regression problems in which the parameter $f$ is the unknown coefficient function of a second order elliptic partial differential operator $L_f$, and the ...
Autor:
Richard Nickl, Evarist Giné
Publikováno v:
Mathematical Foundations of Infinite-Dimensional Statistical Models
In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been develop
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https://doi.org/10.1017/9781009022811
https://doi.org/10.1017/9781009022811
Autor:
Richard Nickl
Bayesian methods based on Gaussian process priors are frequently used in statistical inverse problems arising with partial differential equations (PDEs). They can be implemented by Markov chain Monte Carlo (MCMC) algorithms. The underlying statistica
Publikováno v:
Ann. Statist. 48, no. 1 (2020), 464-490
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by its effecti
Autor:
Richard Nickl, Matteo Giordano
Publikováno v:
Inverse Problems
For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear inverse problem of recovering the conductivity $f>0$ in the divergence form equation $$ \nabla\cdot(f
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https://hdl.handle.net/2318/1901474
https://hdl.handle.net/2318/1901474
Autor:
Richard Nickl, Sven Wang
The problem of generating random samples of high-dimensional posterior distributions is considered. The main results consist of non-asymptotic computational guarantees for Langevin-type MCMC algorithms which scale polynomially in key quantities such
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