Mathematical models provide a quantitative framework with which scientists can assess hypotheses on the potential underlying mechanisms that explain patterns in observed data at different spatial and temporal scales,g...Mathematical models provide a quantitative framework with which scientists can assess hypotheses on the potential underlying mechanisms that explain patterns in observed data at different spatial and temporal scales,generate estimates of key kinetic parameters,assess the impact of interventions,optimize the impact of control strategies,and generate forecasts.We review and illustrate a simple data assimilation framework for calibrating mathematical models based on ordinary differential equation models using time series data describing the temporal progression of case counts relating,for instance,to population growth or infectious disease transmission dynamics.In contrast to Bayesian estimation approaches that always raise the question of how to set priors for the parameters,this frequentist approach relies on modeling the error structure in the data.We discuss issues related to parameter identifiability,uncertainty quantification and propagation as well as model performance and forecasts along examples based on phenomenological and mechanistic models parameterized using simulated and real datasets.展开更多
The identification of load model parameters from practical measurement data has become an essential method to build load models for power system simulation,analysis and control.In practical situations,the accuracy of ...The identification of load model parameters from practical measurement data has become an essential method to build load models for power system simulation,analysis and control.In practical situations,the accuracy of the load model parameters identification results is impacted by data quality and measurement accuracy,which leads to the problem of identifiability.In this paper,an identifiability analysis methodology of load model parameters,by estimating the confidential intervals(CIs)of the parameters,is proposed.The load model structure and the combined optimization and regression method to identify the parameters are first introduced.Then,the definition and analysis method of identifiability are discussed.The CIs of the parameters are estimated through the profile likelihood method,based on which a practical identifiability index(PII)is defined to quantitatively evaluate identifiability.Finally,the effectiveness of the proposed analysis approach is validated by the case study results in a practical provincial power grid.The results show that the impact of various disturbance magnitudes,measurement errors and data length can all be reflected by the proposed PII.Furthermore,the proposed PII can provide guidance in data length selection in practical load model identification situations.展开更多
In this work we fit an epidemiological model SEIAQR(Susceptible-Exposed-Infectious-Asymptomatic-Quarantined-Removed)to the data of the first COVID-19 outbreak in Rio de Janeiro,Brazil.Particular emphasis is given to t...In this work we fit an epidemiological model SEIAQR(Susceptible-Exposed-Infectious-Asymptomatic-Quarantined-Removed)to the data of the first COVID-19 outbreak in Rio de Janeiro,Brazil.Particular emphasis is given to the unreported rate,that is,the proportion of infected individuals that is not detected by the health system.The evaluation of the parameters of the model is based on a combination of error-weighted least squares method and appropriate B-splines.The structural and practical identifiability is analyzed to support the feasibility and robustness of the parameters’estimation.We use the Bootstrap method to quantify the uncertainty of the estimates.For the outbreak of MarcheJuly 2020 in Rio de Janeiro,we estimate about 90%of unreported cases,with a 95%confidence interval(85%,93%).展开更多
基金Authors acknowledge financial support from the NSF grant 1610429 and the NSF grant 1414374 as part of the joint NSFNIH-USDA Ecology and Evolution of Infectious Diseases programUK BiotechnologyBiological Sciences Research Council grant BB/M008894/1 and the Division of International Epidemiology and Population Studies,National Institutes of Health.
文摘Mathematical models provide a quantitative framework with which scientists can assess hypotheses on the potential underlying mechanisms that explain patterns in observed data at different spatial and temporal scales,generate estimates of key kinetic parameters,assess the impact of interventions,optimize the impact of control strategies,and generate forecasts.We review and illustrate a simple data assimilation framework for calibrating mathematical models based on ordinary differential equation models using time series data describing the temporal progression of case counts relating,for instance,to population growth or infectious disease transmission dynamics.In contrast to Bayesian estimation approaches that always raise the question of how to set priors for the parameters,this frequentist approach relies on modeling the error structure in the data.We discuss issues related to parameter identifiability,uncertainty quantification and propagation as well as model performance and forecasts along examples based on phenomenological and mechanistic models parameterized using simulated and real datasets.
基金supported by National Natural Science Foundation of China under Grant No.52107066 and 5210071352.
文摘The identification of load model parameters from practical measurement data has become an essential method to build load models for power system simulation,analysis and control.In practical situations,the accuracy of the load model parameters identification results is impacted by data quality and measurement accuracy,which leads to the problem of identifiability.In this paper,an identifiability analysis methodology of load model parameters,by estimating the confidential intervals(CIs)of the parameters,is proposed.The load model structure and the combined optimization and regression method to identify the parameters are first introduced.Then,the definition and analysis method of identifiability are discussed.The CIs of the parameters are estimated through the profile likelihood method,based on which a practical identifiability index(PII)is defined to quantitatively evaluate identifiability.Finally,the effectiveness of the proposed analysis approach is validated by the case study results in a practical provincial power grid.The results show that the impact of various disturbance magnitudes,measurement errors and data length can all be reflected by the proposed PII.Furthermore,the proposed PII can provide guidance in data length selection in practical load model identification situations.
基金The first and third authors were supported by FAPERJ and CNPq,Brazil.The second author acknowledges the support of the Natural Sciences and Engineering Research Council of Canada(NSERC),funding reference number RGPIN-2021-02632。
文摘In this work we fit an epidemiological model SEIAQR(Susceptible-Exposed-Infectious-Asymptomatic-Quarantined-Removed)to the data of the first COVID-19 outbreak in Rio de Janeiro,Brazil.Particular emphasis is given to the unreported rate,that is,the proportion of infected individuals that is not detected by the health system.The evaluation of the parameters of the model is based on a combination of error-weighted least squares method and appropriate B-splines.The structural and practical identifiability is analyzed to support the feasibility and robustness of the parameters’estimation.We use the Bootstrap method to quantify the uncertainty of the estimates.For the outbreak of MarcheJuly 2020 in Rio de Janeiro,we estimate about 90%of unreported cases,with a 95%confidence interval(85%,93%).
