相关论文: Bayesian inversion for the identification of the d…

Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…

This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…

Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to…

In this work, we are interested in the determination of the shape of the scatterer for the two dimensional time harmonic inverse medium scattering problems in acoustics. The scatterer is assumed to be a piecewise constant function with a…

The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution…

A review of Bayesian restoration of digital images based on Monte Carlo techniques is presented. The topics covered include Likelihood, Prior and Posterior distributions, Poisson, Binay symmetric channel, and Gaussian channel models of…

We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…

The ability to reversibly and site-selectively tune ambipolar doping in a single semiconductor is crucial for reconfigurable electronics beyond silicon, but remains highly challenging. Here, we present a rewritable architecture based on…

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…

Leaving posterior sensitivity concerns aside, non-identifiability of the parameters does not raise a difficulty for Bayesian inference as far as the posterior is proper, but multi-modality or flat regions of the posterior induced by the…

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…

In this work, methods to determine more accurate doping profiles in semiconductors is explored where trap-induced artifacts such as hysteresis and doping artifacts are observed. Specifically in CIGS, it is shown that this fast…

This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…

We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This algorithm sweeps through directions analogously to the…

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…

Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…