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长记忆或中间记忆高斯过程谱密度的贝叶斯非参数估计AI 解读

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. We prove posterior consistency for both $d$ and $g$, under appropriate conditions on the prior…

利用参考先验消除干扰参数AI 解读

The problem of eliminating nuisance parameters is tackled from different points of view. Standard likelihood techniques, such as profile likelihood and its modifications, are compared with a Bayesian analysis based on reference priors (Berger & Bernardo, 1992a). Examples are considered to illustrate what happens in multiparameter problems. In particular the frequentist coverage probabilities of the credible sets derived from the reference priors are shown to be better than…

利用参考先验消除干扰参数AI 解读

The problem of eliminating nuisance parameters is tackled from different points of view. Standard likelihood techniques, such as profile likelihood and its modifications, are compared with a Bayesian analysis based on reference priors (Berger & Bernardo, 1992a). Examples are considered to illustrate what happens in multiparameter problems. In particular the frequentist coverage probabilities of the credible sets derived from the reference priors are shown to be better than…