We consider the problem of estimation and structure learning in a high dimensional normal sequence model, where the underlying parameter vector is piecewise constant, or has a block structure. We develop a Bayesian fusion estimation method by using the Horseshoe prior to induce a strong shrinkage effect on successive differences in the mean parameters, simultaneously imposing sufficient prior concentration for non-zero values of the same. The proposed method thus facilitates consistent estimation and structure recovery of the signal pieces. We provide theoretical justifications of our approach by deriving posterior convergence rates and establishing selection consistency under suitable assumptions. We demonstrate the superior performance of the Horseshoe based Bayesian fusion estimation method through extensive simulations and two real-life examples.

翻译：我们考虑在高维正常序列模型中进行估计和结构学习的问题,在这个模型中,基本参数矢量是小数不变的,或有一个块状结构。我们开发了一种贝叶斯混合估计方法,先使用马蹄,然后对平均参数的连续差异产生强大的缩小效应,同时对非零值规定足够的先前集中,从而有利于对信号碎片进行一致估计和结构回收。我们通过在适当假设下得出后置趋同率和确定选择一致性,为我们的方法提供了理论依据。我们通过广泛的模拟和两个真实例子,展示了基于马蹄的巴耶斯聚变估计方法的优异性。