Recent work on point processes includes studying posterior convergence rates of estimating a continuous intensity function. In this article, convergence rates for estimating the intensity function and change‐point are derived for the more general case of a piecewise continuous intensity function. We study the problem of estimating the intensity function of an inhomogeneous Poisson process with a change‐point using non‐parametric Bayesian methods. An Markov Chain Monte Carlo (MCMC) algorithm is proposed to obtain estimates of the intensity function and the change‐point which is illustrated using simulation studies and applications. The Canadian Journal of Statistics 47: 604–618; 2019 © 2019 Statistical Society of Canada

中文翻译：

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带变化点的非均匀泊松过程的强度函数估计

关于点过程的最新工作包括研究估计连续强度函数的后验收敛率。在本文中，对于分段连续强度函数的更一般情况，得出了用于估计强度函数和变化点的收敛速率。我们研究了使用非参数贝叶斯方法估计具有变化点的非均匀泊松过程的强度函数的问题。提出了一种马尔可夫链蒙特卡洛（MCMC）算法，以获取强度函数和变化点的估计值，并通过仿真研究和应用进行了说明。加拿大统计杂志47：604–618；加拿大统计局。2019©2019加拿大统计学会