The use of some statistical methods for estimating the parameters of ordinary differential equations with practical application

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistics

Presented by researcher

Israa Samad Dwayyeh Al-Safi

Supervised By

Ass. Prof. Dr. Mushtaq Kareem Abd Al-Rahem

Abstract

Ordinary differential equations (ODE) models are widely used to model dynamic processes in many scientific fields, but they usually depend on parameters that are of critical importance in terms of dynamics and need to be estimated directly from the data. Nonlinear Equation Models. In this thesis, the method of non-linear least squares (NLS) was used, which is considered the most common in estimating the parameters of ordinary differential equations and comparing them with the capabilities of the method of maximum a posterior (MAP) using two models of ordinary differential equations. They are both (Malthus model and logistic model) and by employing the Monte Carlo simulation method using five different sample sizes and using the mean square error (MSE) standard, the results concluded that the nonlinear least squares method was more appropriate in estimating the parameters of these models.

And then a practical application was made of real data represented by the number of Iraq’s population for the period (1985-2018) for the purpose of showing the best model in representing these data and using the best methods from the experimental side. His predictions, which are more accurate compared to the Malthus model, where the message found that the population of Iraq will reach 55 million by 2040.

The use of some statistical methods for estimating the parameters of ordinary differential equations with practical application

A Thesis Submitted to

Council of  The Administration and Economics/ Karbala University as Partial fulfillment of the Requirements for the Degree of Master of Science in Statistics

Presented by researcher

Israa Samad Dwayyeh Al-Safi

Supervised By

Ass. Prof. Dr. Mushtaq Kareem Abd Al-Rahem

Abstract

Ordinary differential equations (ODE) models are widely used to model dynamic processes in many scientific fields, but they usually depend on parameters that are of critical importance in terms of dynamics and need to be estimated directly from the data. Nonlinear Equation Models. In this thesis, the method of non-linear least squares (NLS) was used, which is considered the most common in estimating the parameters of ordinary differential equations and comparing them with the capabilities of the method of maximum a posterior (MAP) using two models of ordinary differential equations. They are both (Malthus model and logistic model) and by employing the Monte Carlo simulation method using five different sample sizes and using the mean square error (MSE) standard, the results concluded that the nonlinear least squares method was more appropriate in estimating the parameters of these models.

And then a practical application was made of real data represented by the number of Iraq’s population for the period (1985-2018) for the purpose of showing the best model in representing these data and using the best methods from the experimental side. His predictions, which are more accurate compared to the Malthus model, where the message found that the population of Iraq will reach 55 million by 2040.