Description: Maximum Likelihood Estimation (MLE) is a statistical method used to estimate the parameters of a model based on a set of observed data. Its fundamental principle lies in finding the parameter values that maximize the likelihood function, which measures the probability of observing the data given the model parameters. This approach is particularly valuable in contexts where models need to be fitted to empirical data, as it yields estimates that are asymptotically efficient and consistent. MLE is applied in a variety of statistical models, from linear regressions to more complex models such as mixture models and survival models. One of its distinctive features is that it can be used in situations where data is incomplete or censored, making it a versatile tool in applied statistics. Additionally, MLE can be extended to machine learning contexts, where it is used to optimize parameters in predictive models, thereby improving the accuracy and robustness of predictions. In summary, Maximum Likelihood Estimation is a fundamental pillar in modern statistics, providing a solid framework for statistical inference and data modeling.
History: Maximum Likelihood Estimation was introduced by British statistician Ronald A. Fisher in 1921. Fisher developed this method as part of his work in statistical theory and inference, laying the groundwork for parameter estimation in statistical models. Over the decades, MLE has evolved and established itself as a fundamental technique in statistics, being widely used across various disciplines, from biology to economics.
Uses: Maximum Likelihood Estimation is used in a wide range of applications, including linear and logistic regression, survival models, time series analysis, and mixture models. It is also fundamental in machine learning, where it is applied to fit predictive models and optimize parameters, thereby improving prediction accuracy.
Examples: A practical example of MLE is in logistic regression, where it is used to estimate the coefficients of the model that best predict the probability of a binary event. Another example is in survival analysis, where it is applied to estimate the hazard rate in Cox models.
