TY - JOUR
T1 - MULTISCALE BAYESIAN SURVIVAL ANALYSIS
AU - Castillo, Ismaël
AU - van der Pas, Stéphanie
N1 - Funding Information: Funding. The first author gratefully acknowledges support from the Institut Universitaire de France (IUF) and from the ANR grant ANR-17-CE40-0001 (BASICS). The second author is (partly) financed by the Dutch Research Council (NWO), under Veni grant 192.087. Publisher Copyright: © Institute of Mathematical Statistics, 2021
PY - 2021/12/1
Y1 - 2021/12/1
N2 - We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for ‘many’ functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein–von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these quantities. Further, we show optimal posterior contraction rates for the hazard in terms of the supremum norm. In medical studies, a popular approach is to model hazards a priori as random histograms with possibly dependent heights. This and more general classes of arbitrarily smooth prior distributions are considered as applications of our theory. A sampler is provided for possibly dependent histogram posteriors. Its finite sample properties are investigated on both simulated and real data experiments.
AB - We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for ‘many’ functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein–von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these quantities. Further, we show optimal posterior contraction rates for the hazard in terms of the supremum norm. In medical studies, a popular approach is to model hazards a priori as random histograms with possibly dependent heights. This and more general classes of arbitrarily smooth prior distributions are considered as applications of our theory. A sampler is provided for possibly dependent histogram posteriors. Its finite sample properties are investigated on both simulated and real data experiments.
KW - Frequentist analysis of Bayesian procedures
KW - Nonparametric Bernstein–von Mises theorem
KW - Supremum norm contraction rate
KW - Survival analysis
UR - http://www.scopus.com/inward/record.url?scp=85122219547&partnerID=8YFLogxK
U2 - https://doi.org/10.1214/21-AOS2097
DO - https://doi.org/10.1214/21-AOS2097
M3 - Article
SN - 0090-5364
VL - 49
SP - 3559
EP - 3582
JO - ANNALS OF STATISTICS
JF - ANNALS OF STATISTICS
IS - 6
ER -