Inhomogeneous hidden semi-Markov models for incompletely observed point processes

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Annals of the Institute of Statistical Mathematics Pub Date : 2022-09-18 DOI:10.1007/s10463-022-00843-5

Amina Shahzadi, Ting Wang, Mark Bebbington, Matthew Parry

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引用次数: 1

Abstract

A general class of inhomogeneous hidden semi-Markov models (IHSMMs) is proposed for modelling partially observed processes that do not necessarily behave in a stationary and memoryless manner. The key feature of the proposed model is that the sojourn times of the states in the semi-Markov chain are time-dependent, making it an inhomogeneous semi-Markov chain. Conjectured consistency of the parameter estimators is checked by simulation study using direct numerical optimization of the log-likelihood function. The proposed models are applied to a global volcanic eruption catalogue to investigate the time-dependent incompleteness of the record by introducing a particular case of IHSMMs with time-dependent shifted Poisson state durations and a renewal process as the observed process. The Akaike Information Criterion and residual analysis are used to choose the best model. The selected IHSMM provides useful insights into the completeness of the global record of volcanic eruptions, demonstrating the effectiveness of this method.

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不完全观测点过程的非齐次隐半马尔可夫模型

提出了一类一般的非齐次隐半马尔可夫模型(IHSMMs)，用于模拟部分观察到的过程，这些过程不一定以平稳和无记忆的方式表现。该模型的主要特征是半马尔可夫链中状态的停留时间与时间相关，使其成为非齐次半马尔可夫链。利用对数似然函数的直接数值优化，通过仿真研究验证了参数估计量的推测一致性。将所提出的模型应用于全球火山喷发目录，通过引入具有随时间变化的泊松状态持续时间和更新过程的ihsmm的特定案例来研究记录的时间依赖性不完全性。利用赤池信息准则和残差分析选择最佳模型。所选的IHSMM对全球火山爆发记录的完整性提供了有用的见解，证明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of the Institute of Statistical Mathematics 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.