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Entropy 2015, 17(10), 6576-6597; doi:10.3390/e17106576

Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models

1
Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010,05508-090 São Paulo, Brazil
2
Institute of Mathematics and Statistics, University of Campinas, Rua Sérgio Buarque de Holanda 651, 13083-859 Campinas, Brazil
3
CIMFAV—Facultad de Ingeniería, Universidad de Valparaíso, General Cruz 222, Valparaíso 2362905, Chile
4
Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Av.Libertador Bernardo O'Higgins 3363, Santiago 9170022, Chile
This paper is dedicated to the memory of Professor Francisco Torres-Avilés.
Deceased.
*
Author to whom correspondence should be addressed.
Academic Editors: Carlos Alberto De Bragança Pereira and Adriano Polpo
Received: 28 May 2015 / Revised: 3 September 2015 / Accepted: 15 September 2015 / Published: 25 September 2015
(This article belongs to the Special Issue Inductive Statistical Methods)
View Full-Text   |   Download PDF [530 KB, uploaded 25 September 2015]   |  

Abstract

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. View Full-Text
Keywords: Gamma-modulated process; long memory; Bayesian inference; approximate Bayesian computation; MCMC algorithm; e-value Gamma-modulated process; long memory; Bayesian inference; approximate Bayesian computation; MCMC algorithm; e-value
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Andrade, P.; Rifo, L.; Torres, S.; Torres-Avilés, F. Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models. Entropy 2015, 17, 6576-6597.

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