Bayesian Derivative Order Estimation for a Fractional Logistic Model

Francisco J. Ariza-Hernandez, Martin P. Arciga-Alejandre, Jorge Sanchez-Ortiz and Alberto Fleitas-Imbert
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Francisco J. Ariza-Hernandez: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd. Universitaria. Chilpancingo, Guerrero C.P. 39087, Mexico
Martin P. Arciga-Alejandre: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd. Universitaria. Chilpancingo, Guerrero C.P. 39087, Mexico
Jorge Sanchez-Ortiz: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd. Universitaria. Chilpancingo, Guerrero C.P. 39087, Mexico
Alberto Fleitas-Imbert: Departamento de Matemáticas, Universidad Carlos III de Madrid, Getafe, 28903 Madrid, Spain

Mathematics, 2020, vol. 8, issue 1, 1-9

Abstract: In this paper, we consider the inverse problem of derivative order estimation in a fractional logistic model. In order to solve the direct problem, we use the Grünwald-Letnikov fractional derivative, then the inverse problem is tackled within a Bayesian perspective. To construct the likelihood function, we propose an explicit numerical scheme based on the truncated series of the derivative definition. By MCMC samples of the marginal posterior distributions, we estimate the order of the derivative and the growth rate parameter in the dynamic model, as well as the noise in the observations. To evaluate the methodology, a simulation was performed using synthetic data, where the bias and mean square error are calculated, the results give evidence of the effectiveness for the method and the suitable performance of the proposed model. Moreover, an example with real data is presented as evidence of the relevance of using a fractional model.

Keywords: Bayesian analysis; growth model; Grünwald-Lenikov method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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