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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 OHiggins 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

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





Autor: Plinio Andrade 1, Laura Rifo 2,* , Soledad Torres 3 and Francisco Torres-Avilés 4,‡

Fuente: http://mdpi.com/



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