The likelihood function is a fundamental concept in statistics that measures the plausibility of a statistical model parameter given observed data. It is used extensively in parameter estimation, particularly in maximum likelihood estimation, to identify the values of parameters that maximize the probability of observing the given data.

Likelihood Function

likelihood function

fundamental concept in statistics

plausibility of a statistical model

Observed data refers to information collected through direct measurement or observation of a phenomenon, often used as the foundation for statistical analysis and empirical research. It is crucial for validating hypotheses and building models that reflect real-world conditions and behaviors.

observed data

Parameter estimation is the process of using sample data to infer the values of parameters in a statistical model, which are crucial for making predictions and understanding underlying processes. It involves techniques like point estimation and interval estimation to provide estimates that are as close as possible to the true parameter values of the population being studied.

parameter estimation

Maximum Likelihood Estimation (MLE) is a statistical method for estimating the parameters of a model by maximizing the likelihood function, thereby making the observed data most probable under the assumed statistical model. It is widely used due to its desirable properties such as consistency, efficiency, and asymptotic normality, which make it a cornerstone of statistical inference and machine learning.

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