Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data
In this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali–Mikhail–Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Mar...
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MDPI AG
2018-08-01
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| Online Access: | http://www.mdpi.com/1099-4300/20/9/642 |
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| author | Erlandson Ferreira Saraiva Adriano Kamimura Suzuki Luis Aparecido Milan |
| author_facet | Erlandson Ferreira Saraiva Adriano Kamimura Suzuki Luis Aparecido Milan |
| author_sort | Erlandson Ferreira Saraiva |
| collection | DOAJ |
| description | In this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali–Mikhail–Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Markov Chain (MCMC) algorithms. We present three version of the Metropolis–Hastings algorithm: Independent Metropolis–Hastings (IMH), Random Walk Metropolis (RWM) and Metropolis–Hastings with a natural-candidate generating density (MH). Since the creation of a good candidate generating density in IMH and RWM may be difficult, we also describe how to update a parameter of interest using the slice sampling (SS) method. A simulation study was carried out to compare the performances of the IMH, RWM and SS. A comparison was made using the sample root mean square error as an indicator of performance. Results obtained from the simulations show that the SS algorithm is an effective alternative to the IMH and RWM methods when simulating values from the posterior distribution, especially for small sample sizes. We also applied these methods to a real data set. |
| first_indexed | 2024-12-10T06:59:48Z |
| format | Article |
| id | doaj.art-2d6d894437db4451901054e63c51d5eb |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T06:59:48Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
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| spelling | doaj.art-2d6d894437db4451901054e63c51d5eb2022-12-22T01:58:21ZengMDPI AGEntropy1099-43002018-08-0120964210.3390/e20090642e20090642Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored DataErlandson Ferreira Saraiva0Adriano Kamimura Suzuki1Luis Aparecido Milan2Instituto de Matemática, Universidade Federal de Mato Grosso do Sul, Campo Grande 79070-900, BrazilDepartamento de Matemática Aplicada e Estatística, Universidade de São Paulo, São Carlos 13566-590, BrazilDepartamento de Estatística, Universidade de São Carlos, São Carlos 13565-905, BrazilIn this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali–Mikhail–Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Markov Chain (MCMC) algorithms. We present three version of the Metropolis–Hastings algorithm: Independent Metropolis–Hastings (IMH), Random Walk Metropolis (RWM) and Metropolis–Hastings with a natural-candidate generating density (MH). Since the creation of a good candidate generating density in IMH and RWM may be difficult, we also describe how to update a parameter of interest using the slice sampling (SS) method. A simulation study was carried out to compare the performances of the IMH, RWM and SS. A comparison was made using the sample root mean square error as an indicator of performance. Results obtained from the simulations show that the SS algorithm is an effective alternative to the IMH and RWM methods when simulating values from the posterior distribution, especially for small sample sizes. We also applied these methods to a real data set.http://www.mdpi.com/1099-4300/20/9/642Bayesian inferenceAli–Mikhail–Haq copulaMCMCMetropolis-Hastingsslice sampling |
| spellingShingle | Erlandson Ferreira Saraiva Adriano Kamimura Suzuki Luis Aparecido Milan Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data Entropy Bayesian inference Ali–Mikhail–Haq copula MCMC Metropolis-Hastings slice sampling |
| title | Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data |
| title_full | Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data |
| title_fullStr | Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data |
| title_full_unstemmed | Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data |
| title_short | Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data |
| title_sort | bayesian computational methods for sampling from the posterior distribution of a bivariate survival model based on amh copula in the presence of right censored data |
| topic | Bayesian inference Ali–Mikhail–Haq copula MCMC Metropolis-Hastings slice sampling |
| url | http://www.mdpi.com/1099-4300/20/9/642 |
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