Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach
In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our pr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/25/3/42 |
| _version_ | 1797562874194821120 |
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| author | Yasushi Ota Naoki Mizutani |
| author_facet | Yasushi Ota Naoki Mizutani |
| author_sort | Yasushi Ota |
| collection | DOAJ |
| description | In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model. |
| first_indexed | 2024-03-10T18:33:52Z |
| format | Article |
| id | doaj.art-c7c1604aa25b41a09ba03034f28379d1 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T18:33:52Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-c7c1604aa25b41a09ba03034f28379d12023-11-20T06:23:13ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-07-012534210.3390/mca25030042Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference ApproachYasushi Ota0Naoki Mizutani1Department of Management, Okayama University of Science, 1-1 Ridaicyou, Kita Ward, Okayama 700-0005, JapanDepartment of Management, Okayama University of Science, 1-1 Ridaicyou, Kita Ward, Okayama 700-0005, JapanIn this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model.https://www.mdpi.com/2297-8747/25/3/42societal booms modeltime delaystability of equilibriumBayesian inference approachparameter estimation |
| spellingShingle | Yasushi Ota Naoki Mizutani Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach Mathematical and Computational Applications societal booms model time delay stability of equilibrium Bayesian inference approach parameter estimation |
| title | Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach |
| title_full | Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach |
| title_fullStr | Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach |
| title_full_unstemmed | Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach |
| title_short | Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach |
| title_sort | estimating parameters in mathematical model for societal booms through bayesian inference approach |
| topic | societal booms model time delay stability of equilibrium Bayesian inference approach parameter estimation |
| url | https://www.mdpi.com/2297-8747/25/3/42 |
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