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

Entropy

Plinio Andrade¹  Laura Rifo⁴  Soledad Torres²  Francisco Torres-Avilés³  Carlos Alberto De Bragan๺ Pereira⁵ 

[1] Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010, 05508-090 São Paulo, Brazil; E-Mail:;CIMFAV—Facultad de Ingeniería, Universidad de Valparaíso, General Cruz 222, Valparaíso 2362905, Chile; E-Mail:;Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Av. Libertador Bernardo O’Higgins 3363, Santiago 9170022, Chile;Institute of Mathematics and Statistics, University of Campinas, Rua Sérgio Buarque de Holanda 651, 13083-859 Campinas, Brazil;Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010, 05508-090 São Paulo, Brazil; E-Mail

关键词: Gamma-modulated process;    long memory;    Bayesian inference;    approximate Bayesian computation;    MCMC algorithm;    e-value;   

DOI  :  10.3390/e17106576

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.