Posterior distribution of nondifferentiable functions
研究了参数或半参数模型中不可微函数g(θ)的后验分布的渐近行为，证明在估计量、自助法和后验分布渐近一致时，g(θ)的后验与自助法分布渐近相同，并指出不可微参数的可信区间不能保证是有效置信区间。
This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(θ), where θ is a finite-dimensional parameter of either a parametric or semiparametric model. The main assumption is that the distribution of a suitable estimator θ̂n, its bootstrap approximation, and the Bayesian posterior for θ all agree asymptotically. It is shown that whenever g is locally Lipschitz, though not necessarily differentiable, the posterior distribution of g(θ) and the bootstrap distribution of g(θ̂n) coincide asymptotically. One implication is that Bayesians can interpret bootstrap inference for g(θ) as approximately valid posterior inference in a large sample. Another implication—built on known results about bootstrap inconsistency—is that credible intervals for a nondifferentiable parameter g(θ) cannot be presumed to be approximately valid confidence intervals (even when this relation holds true for θ).