Maximum Likelihood Estimation

In statistics, parameter estimation serves as a fundamental task. One prevalent estimation methodology is Maximum Likelihood Estimation (MLE), which is employed to estimate values of unknown parameters. MLE operates by optimizing the likelihood function, a function derived from the probability density function or probability mass function of given observational data. This optimization typically involves computational techniques such as gradient ascent algorithms or dedicated optimization functions like scipy.optimize.minimize() in Python, where the negative log-likelihood is minimized for numerical stability. Consequently, maximum likelihood estimation constitutes a data-driven statistical inference approach widely applicable across multiple domains including finance, medical research, and engineering applications. The implementation generally requires defining a parametric model, constructing the likelihood function based on observed data, and employing numerical optimization methods to find parameter values that maximize this function.