Credible Distributions of Overall Ranking of Entities
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909923005169664 |
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| author | Chatterjee, Snigdhansu Datta, Gauri Sankar Hou, Yiren Mandal, Abhyuday |
| author_facet | Chatterjee, Snigdhansu Datta, Gauri Sankar Hou, Yiren Mandal, Abhyuday |
| contents | Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity or small area, while precise and accurate estimates of best or worst performing entities are needed for fund allocation, planning and policymaking, stakeholder advocacy, evaluation of welfare programs, and so on. However, ranks estimates constructed exclusively on point estimates of parameters lack uncertainty quantification, and may lead to imbalances and inequities when these are based on small sample sizes. We propose novel Bayesian approaches to address this problem. Our proposals result in partitions of the parameter space with posterior distribution driven partial ordering of the sets in a partition. This in turn translates to a coherent probability mass function over ranks for every entity, and a coherent probability mass function over entities for every rank. Our Bayesian algorithms significantly outperform the state-of-the-art non-Bayesian alternatives, and are amenable to inclusion of covariates in the model as well as borrowing strengths across small areas. We evaluate our proposed Bayesian algorithms in terms of accuracy and stability using a number of applications and a simulation study. Additionally, we develop a novel theoretical framework for inference and ranking problems involving a triangular array of Fay-Herriot models and data, and provide probabilistic guarantees of performances of the proposed Bayesian ranking algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Credible Distributions of Overall Ranking of Entities Chatterjee, Snigdhansu Datta, Gauri Sankar Hou, Yiren Mandal, Abhyuday Methodology Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity or small area, while precise and accurate estimates of best or worst performing entities are needed for fund allocation, planning and policymaking, stakeholder advocacy, evaluation of welfare programs, and so on. However, ranks estimates constructed exclusively on point estimates of parameters lack uncertainty quantification, and may lead to imbalances and inequities when these are based on small sample sizes. We propose novel Bayesian approaches to address this problem. Our proposals result in partitions of the parameter space with posterior distribution driven partial ordering of the sets in a partition. This in turn translates to a coherent probability mass function over ranks for every entity, and a coherent probability mass function over entities for every rank. Our Bayesian algorithms significantly outperform the state-of-the-art non-Bayesian alternatives, and are amenable to inclusion of covariates in the model as well as borrowing strengths across small areas. We evaluate our proposed Bayesian algorithms in terms of accuracy and stability using a number of applications and a simulation study. Additionally, we develop a novel theoretical framework for inference and ranking problems involving a triangular array of Fay-Herriot models and data, and provide probabilistic guarantees of performances of the proposed Bayesian ranking algorithms. |
| title | Credible Distributions of Overall Ranking of Entities |
| topic | Methodology |
| url | https://arxiv.org/abs/2401.01833 |