Bayesian inference provides a natural framework for quantifyinguncertainty in PDE-constrained inverse problems, for fusingheterogeneous sources of information, and for conditioning successivepredictions on data. In this setting, simulating from the posteriorvia Markov chain Monte Carlo (MCMC) constitutes a fundamentalcomputational bottleneck. We...
Creator:
Marzouk, Youssef (Massachusetts Institute of Technology)
Created:
2011-06-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A Bayesian formulation adapted from Kennedy and O'Hagan (2001) andHigdon et al. (2008) is used to give parameter constraints fromphysical observations and a limited number of simulations. The frameworkis based on the idea of replacing the simulator by an emulator whichcan then be used to facilitate computations required for the analysis.In this ...
Creator:
Higdon, David (Los Alamos National Laboratory)
Created:
2011-06-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Biased labelers are a systemic problem in crowdsourcing, and acomprehensive toolbox for handling their responses is still beingdeveloped. A typical crowdsourcing application can be divided intothree steps: data collection, data curation, and learning. At presentthese steps are often treated separately. We present Bayesian BiasMitigation for Crow...
Creator:
Wauthier, Fabian Lutz-Frank (University of California, Berkeley)
Created:
2012-05-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present a Bayesian approach to to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from from heterogeneous sources and provide a quantitative assessment of uncerta...
Creator:
Mallick, Bani K. (Texas A & M University)
Created:
2011-06-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Bayesian denoising of archival film requires a likelihood model that captures the image noise and a spatial prior that captures the statistics of natural scenes. For the former we learn a statistical model of film noise that varies as a function of image brightness. For the latter we use the recently proposed Field-of-Experts framework to learn ...
Creator:
Black, Michael (Brown University)
Created:
2006-02-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
After a brief review of the hierarchical Bayesian viewpoint, I will present examples of interest in the geosciences. The first is a paleoclimate setting. The problem is to use observed temperatures at various depths and the heat equation to infer surface temperature history. The second combines an elementary physical model with observational dat...
Creator:
Berliner, Mark (The Ohio State University)
Created:
2011-06-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Recent developments with polynomial chaos expansions with random coefficients facilitate the accounting for subscale features, not captured in standard probabilistic models. These representations provide a geometric characterization of random variables and processes, which is quite distinct from the characterizations (in terms of probability den...
Creator:
Ghanem, Roger G. (University of Southern California)
Created:
2011-06-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Non-parametric Bayesian techniques are considered for learning dictionaries forsparse image representations, with applications in denoising, inpainting andcompressive sensing (CS). The beta process is employed as a prior for learningthe dictionary, and this non-parametric method naturally infers an appropriatedictionary size. The Dirichlet proce...
Creator:
Carin, Lawrence (Duke University)
Created:
2009-10-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This is a technical talk on the recent marginal-then-conditional sampler for hierarchical Bayesian models. Bayesian models for inverse problems naturally have a hierarchical structure in which the data model depends on a high-dimensional latent structure, which in turn depends on a low-dimensional hyperparameter vector. In the linear-Gaussian ca...
Creator:
Fox, Colin (University of Otago)
Created:
2015-06-19
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.