16.00
|
Bayesian methods for finding structures in complex data objects
Modern data come in the form of all possible complexities. Due to
astonishing advance of technology in the recent years, new forms of data
such as functions, images, curves, shapes, trees or extremely high
dimensional arrays are being encountered and their statistical analysis pose
new challenges. Testing of many hypotheses simultaneously is a new
statistical problem which arise with the huge amount of data collected from
genomic and brain imaging experiments. Understanding these complex data
objects and extracting information from them require finding meaningful
structures described by lower dimensional characteristics which are hidden
under the pile of less useful information. The Bayesian approach offers
probabilistic modeling of those characteristics in the form of a prior
distribution and update the information in the light of the data using Bayes'
theorem. The prior distribution is an effective tool of describing any
qualitative characteristic such as clustering of similar data in hidden
groups. Breakthroughs in computational techniques together with
exponentially increasing computing power allow Bayesian computations to be
performed. We shall describe stochastic processes such as the Chinese
restaurant process and the Indian buffet process as prior distribution for
feature sharing and sparsity, and discuss their use in processing of image
and functional data. We shall also discuss new Bayesian methods for
simultaneous testing of a large number of hypotheses.
Research Interests
Nonparametric Bayesian inference, multiple hypothesis testing, high
dimensional data, ROC analysis, Bayesian imaging, functional data analysis,
noninformative priors, asymptotic properties of the posterior distributions,
nonregular cases, Bayesian computation, nonparametric regression, recur-
rent event data, survival analysis, limit theorems in probability. |