Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach

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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Main Authors: Yasushi Ota, Naoki Mizutani
Format: Article
Language:English
Published: MDPI AG 2020-07-01
Series:Mathematical and Computational Applications
Subjects:
societal booms model
time delay
stability of equilibrium
Bayesian inference approach
parameter estimation
Online Access:https://www.mdpi.com/2297-8747/25/3/42
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spelling doaj-c7c1604aa25b41a09ba03034f28379d12020-11-25T02:59:55ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-07-0125424210.3390/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
collection DOAJ
language English
format Article
sources DOAJ
author Yasushi Ota
Naoki Mizutani
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
author_facet Yasushi Ota
Naoki Mizutani
author_sort Yasushi Ota
title 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_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_sort estimating parameters in mathematical model for societal booms through bayesian inference approach
publisher MDPI AG
series Mathematical and Computational Applications
issn 1300-686X
2297-8747
publishDate 2020-07-01
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.
topic societal booms model
time delay
stability of equilibrium
Bayesian inference approach
parameter estimation
url https://www.mdpi.com/2297-8747/25/3/42
work_keys_str_mv AT yasushiota estimatingparametersinmathematicalmodelforsocietalboomsthroughbayesianinferenceapproach
AT naokimizutani estimatingparametersinmathematicalmodelforsocietalboomsthroughbayesianinferenceapproach
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