Objectif
I propose novel methods for understanding key aspects that are essential
to the future of Bayesian inference for high- or infinite-dimensional
models and data. By combining my expertise on empirical processes and
likelihood theory with my recent work on posterior contraction I shall
foremost lay a mathematical foundation for the Bayesian solution to
uncertainty quantification in high dimensions.
Decades of doubt that Bayesian methods can work for high-dimensional
models or data have in the last decade been replaced by a belief that
these methods are actually especially appropriate in this
setting. They are thought to possess greater capacity for
incorporating prior knowledge and to be better able to combine data
from related measurements. My premise is that for high- or
infinite-dimensional models and data this belief is not well founded,
and needs to be challenged and shaped by mathematical analysis.
My central focus is the accuracy of the posterior distribution as
quantification of uncertainty. This is unclear and has hardly been
studied, notwithstanding that it is at the core of the Bayesian
method. In fact the scarce available evidence on Bayesian credible
sets in high dimensions (sets of prescribed posterior probability)
casts doubt on their ability to capture a given truth. I shall discover
how this depends strongly on the prior distribution, empirical or
hierarchical Bayesian tuning, and posterior marginalizaton, and therewith
generate guidelines for good practice.
I shall study these issues in novel statistical settings (sparsity and
large scale inference, inverse problems, state space models,
hierarchical modelling), and connect to the most recent, exciting
developments in general statistics.
I work against a background of data-analysis in genetics, genomics,
finance, and imaging, and employ stochastic process theory,
mathematical analysis and information theory.
Champ scientifique
Appel à propositions
ERC-2012-ADG_20120216
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Régime de financement
ERC-AG - ERC Advanced GrantInstitution d’accueil
2311 EZ Leiden
Pays-Bas