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广义马尔可夫调制泊松过程的精确且计算高效的贝叶斯推断。

Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes.

作者信息

Gonçalves Flávio B, Dutra Lívia M, Silva Roger W C

机构信息

Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627 - DEST, ICEx, UFMG, Belo Horizonte, Minas Gerais 31270-901 Brazil.

Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, Brazil.

出版信息

Stat Comput. 2022;32(1):14. doi: 10.1007/s11222-021-10074-y. Epub 2022 Jan 6.

DOI:10.1007/s11222-021-10074-y
PMID:35013655
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8733934/
Abstract

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.

摘要

时间点模式的统计建模在多个领域都是一个重要问题。考克斯过程是强度函数为随机函数的泊松过程，是此类数据的常用模型。我们提出了一类新的一维考克斯过程模型，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。引入了一种新颖的方法，基于马尔可夫链蒙特卡罗算法进行精确（直至蒙特卡罗误差）的贝叶斯推断。算法的可靠性取决于经过仔细处理的各种规范，从而产生一种计算效率高（就计算时间而言）的算法，并使其能够用于大数据集。给出了模拟和实际示例来说明该方法的效率和适用性。提出了一个用于拟合流行曲线的特定模型，并用于分析巴西登革热和一些国家新冠疫情的数据。

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