  The initial-final mass relation (IFMR) of white dwarfs (WDs) plays an
important role in stellar evolution. To derive precise estimates of IFMRs and
explore how they may vary among star clusters, we propose a Bayesian
hierarchical model that pools photo- metric data from multiple star clusters.
After performing a simulation study to show the benefits of the Bayesian
hierarchical model, we apply this model to five star clus- ters: the Hyades,
M67, NGC 188, NGC 2168, and NGC 2477, leading to reasonable and consistent
estimates of IFMRs for these clusters. We illustrate how a cluster-specific
analysis of NGC 188 using its own photometric data can produce an unreasonable
IFMR since its WDs have a narrow range of zero-age main sequence (ZAMS) masses.
However, the Bayesian hierarchical model corrects the cluster-specific analysis
by bor- rowing strength from other clusters, thus generating more reliable
estimates of IFMR parameters. The data analysis presents the benefits of
Bayesian hierarchical modelling over conventional cluster-specific methods,
which motivates us to elaborate the pow- erful statistical techniques in this
article.
