scholarly journals Estimate of the rate of unreported COVID-19 cases during the first outbreak in Rio de Janeiro

2021 ◽  
Author(s):  
Maria Soledad ARONNA ◽  
Roberto Guglielmi ◽  
Lucas Machado Moschen
Keyword(s):  
Confidence Interval ◽  
Health System ◽  
Rio De Janeiro ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Bootstrap Method ◽  
Parameters Estimation ◽  
B Splines ◽  
Weighted Least Squares Method ◽  
The Bootstrap Method

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 March-July 2020 in Rio de Janeiro, we estimate about 90% of unreported cases, with a 95% confidence interval (85%, 93%).

scholarly journals Novel Optimization-Based Parameter Estimation Method for the Bass Diffusion Model

SAGE Open ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 215824402110269
Author(s):  
Lang Liang
Keyword(s):  
Parameter Estimation ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Reference Value ◽  
Diffusion Problem ◽  
Bass Model ◽  
Weighted Least Squares Method ◽  
Estimated Parameters ◽  
Bass Diffusion Model

The Bass model is the most popular model for forecasting the diffusion process of a new product. However, the controlling parameters in it are unknown in practice and need to be determined in advance. Currently, the estimation of the controlling parameters has been approached by various techniques. In this case, a novel optimization-based parameter estimation (OPE) method for the Bass model is proposed in the theoretical framework of system dynamics ( SD). To do this, the SD model of the Bass differential equation is first established and then the corresponding optimization mathematical model is formulated by introducing the controlling parameters as design variable and the discrepancy of the adopter function to the reference value as objective function. Using the VENSIM software, the present SD optimization model is solved, and its effectiveness and accuracy are demonstrated by two examples: one involves the exact solution and another is related to the actual user diffusion problem from Chinese Mobile. The results show that the present OPE method can produce higher predicting accuracy of the controlling parameters than the nonlinear weighted least squares method and the genetic algorithms. Moreover, the reliability interval of the estimated parameters and the goodness of fitting of the optimal results are given as well to further demonstrate the accuracy of the present OPE method.

Application of the bootstrap method to quantify uncertainty in seismic hazard estimates

1992 ◽  
Vol 82 (1) ◽  
pp. 104-119
Author(s):  
Michéle Lamarre ◽  
Brent Townshend ◽  
Haresh C. Shah
Keyword(s):  
Confidence Interval ◽  
Seismic Hazard ◽  
Statistical Method ◽  
Bootstrap Method ◽  
Earthquake Magnitude ◽  
Earthquake Catalog ◽  
Uncertainty Measure ◽  
Attenuation Models ◽  
The Bootstrap Method

Abstract This paper describes a methodology to assess the uncertainty in seismic hazard estimates at particular sites. A variant of the bootstrap statistical method is used to combine the uncertainty due to earthquake catalog incompleteness, earthquake magnitude, and recurrence and attenuation models used. The uncertainty measure is provided in the form of a confidence interval. Comparisons of this method applied to various sites in California with previous studies are used to confirm the validity of the method.

scholarly journals Spatial interpolation of daily rainfall at catchment scale: a case study of the Ourthe and Ambleve catchments, Belgium

2010 ◽  
Vol 7 (5) ◽  
pp. 7383-7416 ◽  
Author(s):  
S. Ly ◽  
C. Charles ◽  
A. Degré
Keyword(s):  
Spatial Interpolation ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Daily Rainfall ◽  
Daily Basis ◽  
Catchment Scale ◽  
Geostatistical Methods ◽  
Weighted Least Squares Method ◽  
Thiessen Polygon ◽  
Single Moment

Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (krigings) are widely used in spatial interpolation from point measurement to continuous surfaces. However, the majority of existing geostatistical algorithms are available only for single-moment data. The first step in kriging computation is the semi-variogram modelling which usually uses only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. In this study, we used daily rainfall data from 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, Cressie's Approximate Weighted Least Squares method was used to fit seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) to daily sample semi-variogram on a daily basis. Seven selected raingages were used to compare the interpolation performance of these algorithms applied to many degenerated-raingage cases. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably interpolation with the Thiessen polygon that is commonly used in various hydrological models. Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) presented the highest Root Mean Square Error (RMSE) between the geostatistical and IDW methods. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases.

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