# Bayesian problems

Friday, June 19, 2015 - 11:00am - 12:30pm

Colin Fox (University of Otago)

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 case, of which image deblurring is a canonical example, the full conditional for the latent structure is Gaussian, so can be sampled using efficient methods from numerical linear algebra.

Wednesday, June 17, 2015 - 9:00am - 10:30am

Youssef Marzouk (Massachusetts Institute of Technology), Luis Tenorio (Colorado School of Mines)

Tuesday, June 16, 2015 - 9:00am - 10:30am

Youssef Marzouk (Massachusetts Institute of Technology), Luis Tenorio (Colorado School of Mines)

Wednesday, May 9, 2012 - 1:30pm - 2:30pm

Fabian Wauthier (University of California, Berkeley)

Biased labelers are a systemic problem in crowdsourcing, and a

comprehensive toolbox for handling their responses is still being

developed. A typical crowdsourcing application can be divided into

three steps: data collection, data curation, and learning. At present

these steps are often treated separately. We present Bayesian Bias

Mitigation for Crowdsourcing (BBMC), a Bayesian model to unify all

three. Most data curation methods account for the effects of

labeler bias by modeling all labels as coming from a single latent

comprehensive toolbox for handling their responses is still being

developed. A typical crowdsourcing application can be divided into

three steps: data collection, data curation, and learning. At present

these steps are often treated separately. We present Bayesian Bias

Mitigation for Crowdsourcing (BBMC), a Bayesian model to unify all

three. Most data curation methods account for the effects of

labeler bias by modeling all labels as coming from a single latent

Tuesday, October 6, 2009 - 3:30pm - 4:00pm

Lawrence Carin (Duke University)

Non-parametric Bayesian techniques are considered for learning dictionaries for

sparse image representations, with applications in denoising, inpainting and

compressive sensing (CS). The beta process is employed as a prior for learning

the dictionary, and this non-parametric method naturally infers an appropriate

dictionary size. The Dirichlet process and a probit stick-breaking process are

also considered to exploit structure within an image. The proposed method can

learn a sparse dictionary in situ; training images may be exploited if

sparse image representations, with applications in denoising, inpainting and

compressive sensing (CS). The beta process is employed as a prior for learning

the dictionary, and this non-parametric method naturally infers an appropriate

dictionary size. The Dirichlet process and a probit stick-breaking process are

also considered to exploit structure within an image. The proposed method can

learn a sparse dictionary in situ; training images may be exploited if

Wednesday, June 8, 2011 - 1:00pm - 2:00pm

David Higdon (Los Alamos National Laboratory)

A Bayesian formulation adapted from Kennedy and O'Hagan (2001) and

Higdon et al. (2008) is used to give parameter constraints from

physical observations and a limited number of simulations. The framework

is based on the idea of replacing the simulator by an emulator which

can then be used to facilitate computations required for the analysis.

In this talk I'll describe the details of this approach and apply it

to an example that uses large scale structure of the universe to

inform about a subset of the parameters controlling a

Higdon et al. (2008) is used to give parameter constraints from

physical observations and a limited number of simulations. The framework

is based on the idea of replacing the simulator by an emulator which

can then be used to facilitate computations required for the analysis.

In this talk I'll describe the details of this approach and apply it

to an example that uses large scale structure of the universe to

inform about a subset of the parameters controlling a

Friday, June 10, 2011 - 8:30am - 9:30am

Mark Berliner (The Ohio State University)

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 data in modeling the flow of the Northeast Ice-Stream in Greenland.

Wednesday, June 8, 2011 - 2:30pm - 3:30pm

Youssef Marzouk (Massachusetts Institute of Technology)

Bayesian inference provides a natural framework for quantifying

uncertainty in PDE-constrained inverse problems, for fusing

heterogeneous sources of information, and for conditioning successive

predictions on data. In this setting, simulating from the posterior

via Markov chain Monte Carlo (MCMC) constitutes a fundamental

computational bottleneck. We present a new technique that entirely

avoids Markov chain-based simulation, by constructing a map under

which the posterior becomes the pushforward measure of the

uncertainty in PDE-constrained inverse problems, for fusing

heterogeneous sources of information, and for conditioning successive

predictions on data. In this setting, simulating from the posterior

via Markov chain Monte Carlo (MCMC) constitutes a fundamental

computational bottleneck. We present a new technique that entirely

avoids Markov chain-based simulation, by constructing a map under

which the posterior becomes the pushforward measure of the

Thursday, June 9, 2011 - 2:30pm - 3:30pm

Bani Mallick (Texas A & M University)

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 uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. Karhunen-Lo'eve expansion is used for dimension reduction of the random field.

Thursday, June 9, 2011 - 9:00am - 10:00am

Roger Ghanem (University of Southern California)

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 density functions) typically adapted to Bayesian analysis. Given the importance of Bayes theorem within probability theory, it is important to synthesize the connection between these two representations.