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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2504.01313 |
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| _version_ | 1866913785724272640 |
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| author | Yu, Yian Wang, Bo Shi, Jian Qing |
| author_facet | Yu, Yian Wang, Bo Shi, Jian Qing |
| contents | Motivated by distinct walking patterns in real-world free-living gait data, this paper proposes an innovative curve-based sampling scheme for the analysis of functional data characterized by a mixture of covariance structures. Traditional approaches often fail to adequately capture inherent complexities arising from heterogeneous covariance patterns across distinct subsets of the data. We introduce a unified Bayesian framework that integrates a nonlinear regression function with a continuous-time hidden Markov model, enabling the identification and utilization of varying covariance structures. One of the key contributions is the development of a computationally efficient curve-based sampling scheme for hidden state estimation, addressing the sampling complexities associated with high-dimensional, conditionally dependent data. This paper details the Bayesian inference procedure, examines the asymptotic properties to ensure the structural consistency of the model, and demonstrates its effectiveness through simulated and real-world examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analyzing Functional Data with a Mixture of Covariance Structures Using a Curve-Based Sampling Scheme Yu, Yian Wang, Bo Shi, Jian Qing Methodology Motivated by distinct walking patterns in real-world free-living gait data, this paper proposes an innovative curve-based sampling scheme for the analysis of functional data characterized by a mixture of covariance structures. Traditional approaches often fail to adequately capture inherent complexities arising from heterogeneous covariance patterns across distinct subsets of the data. We introduce a unified Bayesian framework that integrates a nonlinear regression function with a continuous-time hidden Markov model, enabling the identification and utilization of varying covariance structures. One of the key contributions is the development of a computationally efficient curve-based sampling scheme for hidden state estimation, addressing the sampling complexities associated with high-dimensional, conditionally dependent data. This paper details the Bayesian inference procedure, examines the asymptotic properties to ensure the structural consistency of the model, and demonstrates its effectiveness through simulated and real-world examples. |
| title | Analyzing Functional Data with a Mixture of Covariance Structures Using a Curve-Based Sampling Scheme |
| topic | Methodology |
| url | https://arxiv.org/abs/2504.01313 |