Process-augmented lifetime distributions: A generative Bayesian framework for latent structure inference in survival analysis

In survival analysis, the predictive accuracy of lifetime distributions is frequently compromised since the continuous observation assumption is violated, resulting in discretized covariate data. Conventional survival analysis estimators typically address this limitation by treating the observed measurement as the true state or by assuming a mutually independent error structure, complicating the functional predictor that systematically induces discrepancy and obscures particle risk heterogeneity. In this article we propose an alternative Bayesian hierarchical framework, the process-augmented lifetime distribution, which explicitly models the representation gap between the true latent exposure and the observed measurement as a structured, recoverable stochastic process. We construct a generative chain that decomposes the hazard function into an explicit channel spanned by the measurement basis and an orthogonal implicit channel that captures the unobserved variance. This spectral decomposition ensures the identifiability of the latent signal without requiring external validation data by enforcing rigorous orthogonal constraints. We further develop a process augmentation scheme that introduces an intermediate auxiliary variable, transforming the intractable non-Gaussian likelihood into a conjugate structure applicable to an exact Gibbs sampler. This computational formulation permits the derivation of novel posterior functional measurements, which partition the predictive variance into irreducible failure noise and reducible measurement uncertainty. We propose a simulation study and an empirical analysis of high-frequency market stability to confirm that the proposed estimator successfully corrects discrepancy error and resolves intra-bin heterogeneity, providing a robust approach for quantifying structural decision risk in systems subject to severe observation imperfections.