Bayesian Inference for Zero-Modified Power Series Regression Models
Count data often exhibit discrepancies in the frequencies of zeros, which commonly occur across various application domains. These data may include excess zeros (zero inflation) or, less frequently, a scarcity of zeros (zero deflation). In regression models, both situations can arise at different le...
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| Format: | Article |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/60 |
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| author | Katiane S. Conceição Marinho G. Andrade Victor Hugo Lachos Nalini Ravishanker |
| author_facet | Katiane S. Conceição Marinho G. Andrade Victor Hugo Lachos Nalini Ravishanker |
| author_sort | Katiane S. Conceição |
| collection | DOAJ |
| description | Count data often exhibit discrepancies in the frequencies of zeros, which commonly occur across various application domains. These data may include excess zeros (zero inflation) or, less frequently, a scarcity of zeros (zero deflation). In regression models, both situations can arise at different levels of covariates. The zero-modified power series regression model provides an effective framework for modeling such count data, as it does not require prior knowledge of the type of zero modification, whether zero inflation or zero deflation, and can accommodate overdispersion, equidispersion, or underdispersion present in the data. This paper proposes a Bayesian estimation procedure based on the stochastic gradient Hamiltonian Monte Carlo algorithm, effectively addressing many challenges associated with estimating the model parameters. Additionally, we introduce a measure of Bayesian efficiency to evaluate the impact of prior information on parameter estimation. The practical utility of the proposed method is demonstrated through both simulated and real data across different types of zero modification. |
| format | Article |
| id | doaj-art-679dec54dea54087980a104d71ca56f0 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-679dec54dea54087980a104d71ca56f02025-01-10T13:18:07ZengMDPI AGMathematics2227-73902024-12-011316010.3390/math13010060Bayesian Inference for Zero-Modified Power Series Regression ModelsKatiane S. Conceição0Marinho G. Andrade1Victor Hugo Lachos2Nalini Ravishanker3Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, São Carlos 13566-590, SP, BrazilDepartment of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, São Carlos 13566-590, SP, BrazilDepartment of Statistics, University of Connecticut, Storrs, CT 06269, USADepartment of Statistics, University of Connecticut, Storrs, CT 06269, USACount data often exhibit discrepancies in the frequencies of zeros, which commonly occur across various application domains. These data may include excess zeros (zero inflation) or, less frequently, a scarcity of zeros (zero deflation). In regression models, both situations can arise at different levels of covariates. The zero-modified power series regression model provides an effective framework for modeling such count data, as it does not require prior knowledge of the type of zero modification, whether zero inflation or zero deflation, and can accommodate overdispersion, equidispersion, or underdispersion present in the data. This paper proposes a Bayesian estimation procedure based on the stochastic gradient Hamiltonian Monte Carlo algorithm, effectively addressing many challenges associated with estimating the model parameters. Additionally, we introduce a measure of Bayesian efficiency to evaluate the impact of prior information on parameter estimation. The practical utility of the proposed method is demonstrated through both simulated and real data across different types of zero modification.https://www.mdpi.com/2227-7390/13/1/60zero-modified power series modelsSGHMC algorithmBayesian efficiencyBrazilian feminicide notification data |
| spellingShingle | Katiane S. Conceição Marinho G. Andrade Victor Hugo Lachos Nalini Ravishanker Bayesian Inference for Zero-Modified Power Series Regression Models Mathematics zero-modified power series models SGHMC algorithm Bayesian efficiency Brazilian feminicide notification data |
| title | Bayesian Inference for Zero-Modified Power Series Regression Models |
| title_full | Bayesian Inference for Zero-Modified Power Series Regression Models |
| title_fullStr | Bayesian Inference for Zero-Modified Power Series Regression Models |
| title_full_unstemmed | Bayesian Inference for Zero-Modified Power Series Regression Models |
| title_short | Bayesian Inference for Zero-Modified Power Series Regression Models |
| title_sort | bayesian inference for zero modified power series regression models |
| topic | zero-modified power series models SGHMC algorithm Bayesian efficiency Brazilian feminicide notification data |
| url | https://www.mdpi.com/2227-7390/13/1/60 |
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