Survival analysis is widely used for analyzing time-to-event data, and often uncertainty quantification remains challenging in the presence of censoring, limited sample sizes, and heterogeneous populations. Existing Bayesian survival methods provide a framework for incorporating prior information but typically require specification of a full probabilistic likelihood, making inference sensitive to distributional assumptions and sometimes computationally demanding. We propose a Bayesian approach for survival analysis that combines the Bayesian bootstrap with generalized Bayesian (Gibbs) updating. The Bayesian bootstrap first generates a distribution over survival estimators through Dirichlet weights, providing a nonparametric characterization of sampling uncertainty. Prior information for model parameter is then incorporated using a loss function within the generalized Bayesian framework, yielding an inference for posterior distribution. The proposed methodology is model-agnostic and can be applied to a broad class of survival estimators. As an illustration, we develop the framework for the Cox proportional hazards model, producing posterior inference for regression coefficients while preserving the familiar properties and interpretation of hazard ratios. Simulation studies demonstrate that the proposed approach provides robust uncertainty quantification and effectively incorporates prior information. An application to right-censored survival data further illustrates its practical utility. An open-source R package, BayesBoots, implements the proposed methodology.

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