Event Date
SPEAKER: Bo Y.-C. Ning, Visiting Assistant Professor, Statistics, UC Davis
TITLE: "Multiscale Analysis of Bayesian Cox Piecewise Constant Hazards Model"
ABSTRACT: The piecewise constant prior has been routinely in the Bayesian Cox proportional hazards model for survival analysis. Despite its popularity, the large sample properties of this Bayesian method have not yet been fully understood. To fill this gap, we study the posterior distribution from the frequentist perspective using multiscale analysis techniques. Several new results are obtained: first, a joint Bernstein-von Mises theorem for the bivariate linear functionals of the regression coefficients and the baseline hazard. Second, the limiting distribution for the conditional hazard function in the product of $\mathbb{R}^p$ and the appropriate multiscale space. This result leads to the Bayesian Donsker theorems for the conditional cumulative and survival functions. Last, an optimal supremum-norm convergence rate for the posterior of the conditional hazard function is derived. Extensions to the existing framework of studying the nonparametric Bernstein-von Mises phenomenon are made to obtain our results for joint posterior distributions.Those extensions can serve as a useful tool to study other semi- and nonparametric models in the future. Simulation studies for finite sample datasets are conducted to verify our theory. Their results also demonstrate the Bayesian method is a competitive alternative to the frequentist approach.
DATE: Thursday December 2nd, 2021
LOCATION: MSB 1147, Colloquium Room*
*This will be an in-person seminar and is open to the public. STA 290 registrants are required to attend in person. For others, there will be a Zoom link available if you choose to listen in to the seminar remotely. To access the Zoom meeting for this seminar, please contact the instructor Professor Drake or Pete Scully ([email protected]) for the meeting ID and password, stating your affiliation.