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InfiniteBayesian

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Bayesian Statistics in Infinite Dimensions TargetingPriors by Mathematical Anal...

Bayesian Statistics in Infinite Dimensions TargetingPriors by Mathematical Analysis 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 theor... ver más

30/04/2018

ULEI

2M€

Presupuesto del proyecto: 2M€

Líder del proyecto

UNIVERSITEIT LEIDEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2018-04-30 No tenemos la información de la convocatoria

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Líder del proyecto

UNIVERSITEIT LEIDEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto 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 Decades of doubt that Bayesian methods can work for high-dimensional models or data have in the last decade been replaced by a belief that these methods are actually especially appropriate in this setting.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.

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