Bayesian Derivative Order Estimation for a Fractional Logistic Model
Abstract
:1. Introduction
2. The Model
- A fractional differential equation given by
- A statistical model given by
3. Bayesian Estimation
4. Simulation
- We calculated the MAP estimators of the parameters for the models and . To make inference, we use a total of 2000 iterations for each parameter of interest, with two chains of length 10,000 each one. We propose the following weakly informative prior distributions [24],
- From the 1000 samples, we obtained measures of the bias and mean-squared error of the estimators.
5. Illustrative Example
6. Concluding Remarks
Author Contributions
Funding
Conflicts of Interest
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Sample Size | Parameter | ||||
---|---|---|---|---|---|
Bias | MSE | Bias | MSE | ||
a | −0.00048 | 0.00004 | 0.446 | 0.199 | |
−0.00088 | 0.00005 | — | — | ||
−0.01410 | 0.00021 | −0.288 | 0.081 | ||
a | 0.00042 | 0.00006 | 0.283 | 0.082 | |
−0.00037 | 0.00001 | — | — | ||
−0.01350 | 0.00019 | −0.190 | 0.037 | ||
a | 0.00083 | 0.00007 | 0.145 | 0.022 | |
−0.00097 | 0.00014 | — | — | ||
−0.01330 | 0.00019 | −0.086 | 0.008 | ||
a | −0.00014 | 0.00002 | 0.433 | 0.188 | |
−0.00004 | 0.00003 | — | — | ||
−0.00710 | 0.00006 | −0.310 | 0.095 | ||
a | 0.00049 | 0.00002 | 0.294 | 0.087 | |
−0.00022 | 0.00005 | — | — | ||
−0.00640 | 0.00005 | −0.178 | 0.032 | ||
a | 0.00074 | 0.000035 | 0.178 | 0.032 | |
−0.00052 | 0.00830 | — | — | ||
−0.00650 | 0.00005 | −0.069 | 0.005 |
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Ariza-Hernandez, F.J.; Arciga-Alejandre, M.P.; Sanchez-Ortiz, J.; Fleitas-Imbert, A. Bayesian Derivative Order Estimation for a Fractional Logistic Model. Mathematics 2020, 8, 109. https://doi.org/10.3390/math8010109
Ariza-Hernandez FJ, Arciga-Alejandre MP, Sanchez-Ortiz J, Fleitas-Imbert A. Bayesian Derivative Order Estimation for a Fractional Logistic Model. Mathematics. 2020; 8(1):109. https://doi.org/10.3390/math8010109
Chicago/Turabian StyleAriza-Hernandez, Francisco J., Martin P. Arciga-Alejandre, Jorge Sanchez-Ortiz, and Alberto Fleitas-Imbert. 2020. "Bayesian Derivative Order Estimation for a Fractional Logistic Model" Mathematics 8, no. 1: 109. https://doi.org/10.3390/math8010109
APA StyleAriza-Hernandez, F. J., Arciga-Alejandre, M. P., Sanchez-Ortiz, J., & Fleitas-Imbert, A. (2020). Bayesian Derivative Order Estimation for a Fractional Logistic Model. Mathematics, 8(1), 109. https://doi.org/10.3390/math8010109