Application of maximum likelihood estimation in various mathematical models

Maximum likelihood estimation is a breakthrough in the history of statistics, which overcomes the main weakness of Bayesian estimation and has been widely used in various fields, such as language and image processing, and system identification, etc. This paper analyzes the application of maximum likelihood estimation on different mathematical models. It is proved that the universality of maximum likelihood estimation plays an important role in promoting the continued in-depth research on maximum likelihood estimation. This paper also analyzes and summarizes the application of maximum likelihood estimation to specific parameters in different mathematical models. In addition, this work conducts research on the application conditions of maximum likelihood estimation and its main properties, such as variability, consistency, and asymptotic normality, etc. In different mathematical models, such as the annealing furnace efficiency system, gamma environmental factors and adaptive algorithm, etc. Therefore, this paper finds the reason for why the maximum likelihood estimate is widely used in various fields.