The chapter provides a review of Bayesian adaptation which generally refers to the property of prior distributions on function spaces to lead to minimax-optimal (up to logarithmic factors) posterior contraction rates at the distribution generating the data, regardless of whether the value of a model hyperparameter describing some structural attribute (typically the regularity level or the smoothness degree) of the function being estimated is known or not.
Bayesian adaptation
Catia Scricciolo
2024-01-01
Abstract
The chapter provides a review of Bayesian adaptation which generally refers to the property of prior distributions on function spaces to lead to minimax-optimal (up to logarithmic factors) posterior contraction rates at the distribution generating the data, regardless of whether the value of a model hyperparameter describing some structural attribute (typically the regularity level or the smoothness degree) of the function being estimated is known or not.
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