On Stable Parameter Estimation and Forecasting in Epidemiology by the Levenberg–Marquardt Algorithm with Broyden’s Rank-one Updates for the Jacobian Operator

A comparison between artificial neural network (ANN) and multiple linear regression (MLR) models was employed to predict the heat of combustion, and the gross and net heat values, of a diesel fuel engine, based on the chemical composition of the diesel fuel. One hundred and fifty samples of Iraqi diesel provided data from chromatographic analysis. Eight parameters were applied as inputs in order to predict the gross and net heat combustion of the diesel fuel. A trial-and-error method was used to determine the shape of the individual ANN. The results showed that the prediction accuracy of the ANN model was greater than that of the MLR model in predicting the gross heat value. The best neural network for predicting the gross heating value was a back-propagation network (8-8-1), using the Levenberg�Marquardt algorithm for the second step of network training. R = 0.98502 for the test data. In the same way, the best neural network for predicting the net heating value was a back-propagation network (8-5-1), using the Levenberg�Marquardt algorithm for the second step of network training. R = 0.95112 for the test data.

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Prediction of discharge through a sharp-crested triangular weir using ANN model trained with Levenberg–Marquardt algorithm

Modeling Earth Systems and Environment ◽

10.1007/s40808-021-01167-8 ◽

2021 ◽

Author(s):

Md. Shaheer Ali ◽

Md. Ayaz ◽

Talib Mansoor

Keyword(s):

Ann Model ◽

Marquardt Algorithm ◽

Levenberg Marquardt

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MLE-Based Parameter Estimation for Four-Parameter Exponential Gamma Distribution and Asymptotic Variance of Its Quantiles

Water ◽

10.3390/w13152092 ◽

2021 ◽

Vol 13 (15) ◽

pp. 2092

Author(s):

Songbai Song ◽

Yan Kang ◽

Xiaoyan Song ◽

Vijay P. Singh

Keyword(s):

Parameter Estimation ◽

Confidence Intervals ◽

Asymptotic Variance ◽

Information Matrix ◽

Estimation Method ◽

Flood Frequency Analysis ◽

Annual Precipitation ◽

Precipitation Data ◽

Marquardt Algorithm ◽

Design Values

The choice of a probability distribution function and confidence interval of estimated design values have long been of interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) distribution has been developed for application in hydrology, its maximum likelihood estimation (MLE)-based parameter estimation method and asymptotic variance of its quantiles have not been well documented. In this study, the MLE method was used to estimate the parameters and confidence intervals of quantiles of the FPEG distribution. This method entails parameter estimation and asymptotic variances of quantile estimators. The parameter estimation consisted of a set of four equations which, after algebraic simplification, were solved using a three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix and Fisher’s expected information matrix, derivatives of the design quantile with respect to the parameters were derived. The method of estimation was applied to annual precipitation data from the Weihe watershed, China and confidence intervals for quantiles were determined. Results showed that the FPEG was a good candidate to model annual precipitation data and can provide guidance for estimating design values

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