TY - GEN

T1 - Local posterior concentration rate for multilevel sparse sequences

AU - Belitser, E.N.

AU - Nurushev, N.

PY - 2017

Y1 - 2017

N2 - We consider empirical Bayesian inference in the many normal means model in the situation when the high-dimensional mean vector is multilevel sparse, that is, most of the entries of the parameter vector are some fixed values. For instance, the traditional sparse signal is a particular case (with one level) of multilevel sparse sequences. We apply an empirical Bayesian approach, namely we put an appropriate prior modeling the multilevel sparsity and make data-dependent choices of certain parameters of the prior. We establish local (i.e., with rate depending on the “true” parameter) posterior contraction and estimation results. Global adaptive minimax results (for the estimation and posterior contraction problems) over sparsity classes follow from our local results if the sparsity level is of polynomial order. The results are illustrated by simulations.

AB - We consider empirical Bayesian inference in the many normal means model in the situation when the high-dimensional mean vector is multilevel sparse, that is, most of the entries of the parameter vector are some fixed values. For instance, the traditional sparse signal is a particular case (with one level) of multilevel sparse sequences. We apply an empirical Bayesian approach, namely we put an appropriate prior modeling the multilevel sparsity and make data-dependent choices of certain parameters of the prior. We establish local (i.e., with rate depending on the “true” parameter) posterior contraction and estimation results. Global adaptive minimax results (for the estimation and posterior contraction problems) over sparsity classes follow from our local results if the sparsity level is of polynomial order. The results are illustrated by simulations.

KW - Empirical Bayesian approach

KW - Local posterior concentration rate

KW - Multilevel sparse sequences

UR - http://www.scopus.com/inward/record.url?scp=85020029179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020029179&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-54084-9_6

DO - 10.1007/978-3-319-54084-9_6

M3 - Conference contribution

SN - 9783319540832

T3 - Springer Proceedings in Mathematics and Statistics

SP - 51

EP - 66

BT - Bayesian Statistics in Action

A2 - Argiento, Raffaele

A2 - Lanzarone, Ettore

A2 - Antoniano Villalobos, Isadora

A2 - Mattei, Alessandra

PB - Springer

ER -