Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach
Abstract
:1. Introduction
2. Mathematical Model
2.1. Three Key Points to Derive Our Proposed Model
2.2. Mathematical Model for Societal Booms
- State1 Pre-boom: Condition where there is a potential to adopt a boom.
- State2 On-boom: Condition where the boom is captured.
- State3 Rooted-boom: Condition where the boom is retained.
- State4 Unrooted -boom: Condition where the boom did not take off.
3. Stability of the Equilibrium Point for the Reduced Model
4. Bayesian Inference Approach for Estimating Parameters
Markov Chain Monte Carlo Methods (MCMC)
- Step1: Generate (the normal distribution) with a given stander derivation for given .
- Step2: Calculate the choice .
- Step3: Update as with probability but otherwise set .
5. Using Real Data to Evaluate Validity of Proposed Model
5.1. Parameter Estimation Steps
5.2. Coefficient of Determination
5.3. Model Fitting to Actual Data
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Lalaland | |||||
---|---|---|---|---|---|
0.0001 | 6700 | ||||
0.001 | 0 | ||||
0.01 | 1792 | ||||
0.001 | 0 | ||||
0.001 | 14 | ||||
0.001 | 405 |
Pure_Water | |||||
---|---|---|---|---|---|
0.0001 | 19,000 | ||||
0.01 | 0 | ||||
0.01 | 1207 | ||||
0.01 | 0 | ||||
0.01 | 14 | ||||
0.01 | 72 |
Honkirin Beer | |||||
---|---|---|---|---|---|
0.0001 | 4700 | ||||
0.01 | 0 | ||||
0.01 | 63 | ||||
0.01 | 0 | ||||
0.01 | 48 | ||||
0.01 | 158 |
Cupnoodle | |||||
---|---|---|---|---|---|
0.0001 | 8200 | ||||
0.01 | 0 | ||||
0.01 | 1633 | ||||
0.01 | 0 | ||||
0.01 | 11 | ||||
0.01 | 444 |
Beautiful_Harmony | |||||
---|---|---|---|---|---|
0.00001 | 2,700,000 | ||||
0.01 | 0 | ||||
0.01 | 0 | ||||
0.01 | 0 | ||||
0.01 | 10 | ||||
0.01 | 62 |
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Ota, Y.; Mizutani, N. Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach. Math. Comput. Appl. 2020, 25, 42. https://doi.org/10.3390/mca25030042
Ota Y, Mizutani N. Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach. Mathematical and Computational Applications. 2020; 25(3):42. https://doi.org/10.3390/mca25030042
Chicago/Turabian StyleOta, Yasushi, and Naoki Mizutani. 2020. "Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach" Mathematical and Computational Applications 25, no. 3: 42. https://doi.org/10.3390/mca25030042