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Abstract:
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The Bayesian approach to analyzing semiparametric models are gaining popularity in practice. However, except for one-dimensional linear regression with an unknown error distribution and binary response regression with unknown link function, even consistency of Bayesian procedures has not been studied for a general prior. We consider consistency of Bayesian inference for several semiparametric models including multiple linear regression with an unknown error distribution, exponential frailty model, generalized linear model with unknown link function, Cox proportional hazard model with unknown baseline hazard function, accelerated failure time model and partial linear regression model. We give sufficient conditions under which the posterior of the parametric part is consistent in the Euclidean distance while the nonparametric part is consistent w.r.t.some topology such as weak topology.
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