Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models
In this work, we propose a Bayesian methodology to make inferences for the memory parameter and other characteristics under non-standard assumptions for a class of stochastic processes. This class generalizes the Gamma-modulated process, with trajectories that exhibit long memory behavior, as well a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-09-01
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| Online Access: | http://www.mdpi.com/1099-4300/17/10/6576 |
| _version_ | 1798039850239131648 |
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| author | Plinio Andrade Laura Rifo Soledad Torres Francisco Torres-Avilés |
| author_facet | Plinio Andrade Laura Rifo Soledad Torres Francisco Torres-Avilés |
| author_sort | Plinio Andrade |
| collection | DOAJ |
| description | In this work, we propose a Bayesian methodology to make inferences for the memory parameter and other characteristics under non-standard assumptions for a class of stochastic processes. This class generalizes the Gamma-modulated process, with trajectories that exhibit long memory behavior, as well as decreasing variability as time increases. Different values of the memory parameter influence the speed of this decrease, making this heteroscedastic model very flexible. Its properties are used to implement an approximate Bayesian computation and MCMC scheme to obtain posterior estimates. We test and validate our method through simulations and real data from the big earthquake that occurred in 2010 in Chile. |
| first_indexed | 2024-04-11T21:59:22Z |
| format | Article |
| id | doaj.art-46fb226929ce48c997f221da536f44a4 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T21:59:22Z |
| publishDate | 2015-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-46fb226929ce48c997f221da536f44a42022-12-22T04:01:00ZengMDPI AGEntropy1099-43002015-09-0117106576659710.3390/e17106576e17106576Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression ModelsPlinio Andrade0Laura Rifo1Soledad Torres2Francisco Torres-Avilés3Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010,05508-090 São Paulo, BrazilInstitute of Mathematics and Statistics, University of Campinas, Rua Sérgio Buarque de Holanda 651, 13083-859 Campinas, BrazilCIMFAV—Facultad de Ingeniería, Universidad de Valparaíso, General Cruz 222, Valparaíso 2362905, ChileDepartamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Av.Libertador Bernardo O'Higgins 3363, Santiago 9170022, ChileIn this work, we propose a Bayesian methodology to make inferences for the memory parameter and other characteristics under non-standard assumptions for a class of stochastic processes. This class generalizes the Gamma-modulated process, with trajectories that exhibit long memory behavior, as well as decreasing variability as time increases. Different values of the memory parameter influence the speed of this decrease, making this heteroscedastic model very flexible. Its properties are used to implement an approximate Bayesian computation and MCMC scheme to obtain posterior estimates. We test and validate our method through simulations and real data from the big earthquake that occurred in 2010 in Chile.http://www.mdpi.com/1099-4300/17/10/6576Gamma-modulated processlong memoryBayesian inferenceapproximate Bayesian computationMCMC algorithme-value |
| spellingShingle | Plinio Andrade Laura Rifo Soledad Torres Francisco Torres-Avilés Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models Entropy Gamma-modulated process long memory Bayesian inference approximate Bayesian computation MCMC algorithm e-value |
| title | Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models |
| title_full | Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models |
| title_fullStr | Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models |
| title_full_unstemmed | Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models |
| title_short | Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models |
| title_sort | bayesian inference on the memory parameter for gamma modulated regression models |
| topic | Gamma-modulated process long memory Bayesian inference approximate Bayesian computation MCMC algorithm e-value |
| url | http://www.mdpi.com/1099-4300/17/10/6576 |
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