Abstract
We study a Bayesian approach to the inference of an event time distribution in the current status model where observation times are supported on a grid of potentially unknown sparsity and multiple subjects share the same observation time. The model leads to a very simple likelihood, but statistical inferences are non-trivial due to the unknown sparsity of the grid. In particular, for an inference based on the maximum likelihood estimator, one needs to estimate the density of the event time distribution which is challenging because the event time is not directly observed. We consider Bayes procedures with a Dirichlet prior on the event time distribution. With this prior, the Bayes estimator and credible sets can be easily computed via a Gibbs sampler algorithm. Our main contribution is to provide thorough investigation of frequentist’s properties of the posterior distribution. Specifically, it is shown that the posterior convergence rate is adaptive to the unknown sparsity of the grid. If the grid is sufficiently sparse, we further prove the Bernstein–von Mises theorem which guarantees frequentist’s validity of Bayesian credible sets. A numerical study is also conducted for illustration.
Funding Statement
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A4A1031019).
Acknowledgements
The author is grateful for the comments of reviewers on an earlier version of the paper. He also thanks to Runlong Tang for sharing his code, and Dipankar Bandyopadhyay for introducing the paper Tang, Banerjee and Kosorok (2012)
Citation
Minwoo Chae. "Adaptive Bayesian inference for current status data on a grid." Bernoulli 29 (1) 403 - 427, February 2023. https://doi.org/10.3150/22-BEJ1462
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