Bayesian Sequential Inference in Dynamic Survival Models
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Dynamic hazard models are applied to analyze time-varying effects of covariates on the survival time. The state-of-the-art methods for learning parameters in the Bayesian framework are MCMC methods but due to high correlations among the time-varying effect parameters, they converge very slowly. To handle these correlations efficiently, we apply a Sequential Monte Carlo (SMC) method commonly known as Particle Filter (PF). We develop a proposal distribution tailored to the nature of the survival data based on the second order Taylor series expansion of the posterior distribution and the linear Bayes theory. Our PF based sampler is shown to be faster and generates an effective sample size that is more than two orders of magnitude larger than a state-of-the-art MCMC sampler for the same computing time.
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