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首页> 外文期刊>Electronic Journal of Statistics >Posterior convergence and model estimation in Bayesian change-point problems
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Posterior convergence and model estimation in Bayesian change-point problems

机译：贝叶斯变化点问题的后验收敛和模型估计

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We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the rate up to some logarithmic factor, showing the parametric rate of convergence of the posterior distribution requires additional work and assumptions. Additionally, we demonstrate the asymptotic normality of the segment levels under these assumptions. For inferences on the number of change-points, we show that the Bayesian approach can produce a consistent posterior estimate. Finally, we show that consistent posterior for model selection necessarily implies that the parametric rate for posterior estimation stated previously cannot be uniform over the class of models we consider. This is the Bayesian version of the same phenomenon that has been noted and studied by other authors.
机译：当变化点的数量和位置未知时，我们研究贝叶斯多变化点回归问题的后验分布。尽管应用一般理论相对容易地获得不超过一定对数因子的比率，但是显示后验分布的参数收敛速度需要额外的工作和假设。另外，我们在这些假设下证明了分段水平的渐近正态性。对于变化点数量的推断，我们表明贝叶斯方法可以产生一致的后验估计。最后，我们证明了用于模型选择的一致后验必然意味着，在我们考虑的模型类别上，先前所述的后验估计参数率不可能统一。这是其他作者已经注意到和研究的同一现象的贝叶斯版本。

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