Kernel density estimate predictives converge weakly almost surely (hence are asymptotically exchangeable) even though they are neither c.i.d. nor a.c.i.d., and for Gaussian kernels the limit is a.s. absolutely continuous, enabling density credibility intervals.
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Posterior uncertainty for kernel density estimates
Kernel density estimate predictives converge weakly almost surely (hence are asymptotically exchangeable) even though they are neither c.i.d. nor a.c.i.d., and for Gaussian kernels the limit is a.s. absolutely continuous, enabling density credibility intervals.