MAXIMUM LIKELIHOOD Meaning and
Definition
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Maximum likelihood is a statistical concept used to estimate the parameters of a probability distribution or a statistical model. It provides a method to determine the values of these parameters that maximize the likelihood, or the probability, of the observed data occurring given the assumed model.
In the context of parameter estimation, maximum likelihood seeks to find the set of parameter values that make the observed data most likely under the assumed model. The likelihood function, which captures the probability distribution of the data given the parameters, is maximized to obtain the estimates. This often involves finding the partial derivatives of the likelihood function with respect to each parameter and setting them equal to zero, solving for the parameter values that maximize the likelihood.
The maximum likelihood estimation (MLE) method can be applied to various statistical models, including continuous and discrete distributions, regression models, and machine learning algorithms. MLE provides a rigorous and widely used framework for parameter estimation, as it is based on strong statistical foundations and can be mathematically derived in many cases. However, it requires certain assumptions about the data and the model, such as independence and identically distributed observations.
In summary, maximum likelihood is a statistical technique that estimates the parameters of a model by finding the values that make the observed data most likely under that model. It enables precise parameter estimation and is applicable across various statistical models.
Common Misspellings for MAXIMUM LIKELIHOOD
Etymology of MAXIMUM LIKELIHOOD
The etymology of the term "maximum likelihood" can be understood by breaking it down into its individual parts:
1. Maximum: The word "maximum" comes from the Latin word "maximum", meaning "greatest" or "largest". It is derived from the Latin word "maximus", which serves as a superlative form of "magnus", meaning "great" or "large". In the context of statistics, "maximum" refers to the highest or optimal value.
2. Likelihood: The word "likelihood" comes from the Middle English word "liklihood", which means "probability" or "chance". It is derived from the Old English word "gelic", meaning "similar" or "like". In the context of statistics, "likelihood" refers to the probability or plausibility of a certain event or data.
