Maximum Likelihood

Maximum likelihood estimation (MLE) is a fundamental statistical method for estimating the parameters of a probability distribution by maximizing the likelihood of observing the data. Current research focuses on improving MLE's efficiency and robustness, particularly in high-dimensional settings and for complex models like mixture models and latent variable models, often employing techniques like score matching, variational inference, and novel optimization algorithms (e.g., particle swarm optimization, Dykstra-like splitting). These advancements address computational challenges and improve the accuracy and applicability of MLE across diverse fields, from machine learning and signal processing to psychometrics and spatial statistics.