A Bayesian justification of Cox's partial likelihood

In this paper, we establish both naive and formal Bayesian Justifications of Cox's ( 1975) partial likelihood and its various modifications. We extend the original work of Kalbfieisch (1978), who showed that the partial likelihood is a limiting marginal posterior under noninformative priors for baseline hazards. We extend the result to scenarios with time-dependent covariates and time-varying regression parameters. We establish results for continuous time as well as grouped survival data. In addition, we present a Bayesian justification of a modified partial likelihood for handling ties. We also present tools for simplification of the Gibbs sampling algorithm for implementing partial likelihood based Bayeslan inference in various practical applications.