Well-Posed Bayesian Inverse Problems: Priors with Exponential Tails
نویسندگان
چکیده
منابع مشابه
Ill-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
متن کاملEstimating Bayesian Decision Problems with Heterogeneous Priors
In many areas of economics there is a growing interest in how expertise and preferences drive individual and group decision making under uncertainty. Increasingly, we wish to estimate such models to quantify which of these drive decision making. In this paper we propose a new channel through which we can empirically identify expertise and preference parameters by using variation in decisions ov...
متن کاملLearning, Regularization and Ill-Posed Inverse Problems
Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we pro...
متن کاملA Scalable Algorithm for Map Estimators in Bayesian Inverse Problems with Besov Priors
We present a scalable solver for approximating the maximum a posteriori (MAP) point of Bayesian inverse problems with Besov priors based on wavelet expansions with random coefficients. It is a subspace trust region interior reflective Newton conjugate gradient method for bound constrained optimization problems. The method combines the rapid locally-quadratic convergence rate properties of Newto...
متن کاملHybrid Samplers for Ill-Posed Inverse Problems
In the Bayesian approach to ill-posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distrib...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM/ASA Journal on Uncertainty Quantification
سال: 2017
ISSN: 2166-2525
DOI: 10.1137/16m1076824