Statistical modeling of temporal point patterns is an important problem in several areas. The Cox process, a Poisson process where the intensity function is stochastic, is a common model for such data. We present a new class of unidimensional Cox process models in which the intensity function assumes parametric functional forms that switch according to a continuous-time Markov chain. A novel methodology is introduced to perform exact (up to Monte Carlo error) Bayesian inference based on MCMC algorithms. The reliability of the algorithms depends on a variety of specifications which are carefully addressed, resulting in a computationally efficient (in terms of computing time) algorithm and enabling its use with large data sets. Simulated and real examples are presented to illustrate the efficiency and applicability of the methodology. A specific model to fit epidemic curves is proposed and used to analyze data from Dengue Fever in Brazil and COVID-19 in some countries.

时间点模式的统计建模是几个领域的一个重要问题。Cox 过程是强度函数是随机的泊松过程，是此类数据的常用模型。我们提出了一类新的一维 Cox 过程模型，其中强度函数采用根据连续时间马尔可夫链切换的参数函数形式。引入了一种新的方法来执行基于 MCMC 算法的精确（直至蒙特卡洛误差）贝叶斯推理。算法的可靠性取决于经过仔细处理的各种规范，从而产生计算效率（在计算时间方面）的算法，并使其能够用于大型数据集。给出了模拟和真实的例子来说明该方法的效率和适用性。