Adaptive Bayesian estimation in Gaussian sequence space models

Johannes, Jan;Schenk, Rudolf;Simoni, Anna
(2014) , 14 pages

Files

ISBADP201406.pdf
  • Open Access
  • Adobe PDF
  • 330.12 KB
Download

Details

Authors
  • Johannes, JanUCLouvain
    Author
  • Schenk, RudolfUCLouvain
    Author
  • Simoni, AnnaUniversité de Cergy-Pontoise
    Author
Abstract
We consider the inverse problem of recovering a signal in a Gaussian sequence space model (GSSM). We adopt a Bayes procedure and study its frequentist properties. We first derive lower and upper bounds for the posterior concentration rate over a family of Gaussian prior distributions indexed by a tuning parameter m. Under a suitable choice of m we derive a concentration rate uniformly over a class of parameters and show that this rate coincides with the minimax rate. Then, we construct a hierarchical fully data-driven Bayes procedure and show that it is minimax adaptive.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Johannes, J., Schenk, R., & Simoni, A. (2014). Adaptive Bayesian estimation in Gaussian sequence space models (ISBA Discussion Paper 2014/06). https://hdl.handle.net/2078.5/200402