A computational tool that determines parameter values for a statistical model based on observed data. This tool aims to find the set of parameters that maximize the likelihood function, which represents the probability of observing the given data, assuming the model is correct. For example, if one has a set of measurements assumed to follow a normal distribution, the tool calculates the mean and standard deviation that make the observed data most probable.
Such a tool is valuable for statistical inference and data analysis across various disciplines. It offers a systematic approach to parameter estimation, providing results with desirable statistical properties, particularly when the sample size is large. Its origins lie in the development of statistical theory, with early contributions laying the foundation for modern estimation methods. These techniques are essential for deriving statistically robust insights from data.
