likelihoodestimation
Likelihood estimation is a method of parameter estimation that uses the likelihood function L(θ|x) = ∏ f(x_i|θ) for a parametric model. The likelihood is viewed as a function of θ given the observed data x, not of the data given θ. The aim is to identify parameter values that maximize L.
Maximum likelihood estimation (MLE) is the standard approach: θ_hat = argmax_θ L(θ|x). In practice log-likelihood l(θ)=log L
Invariance and examples: MLEs are invariant under reparameterization: if φ=g(θ), then φ_hat=g(θ_hat). A simple example: coin
Extensions and computation: for incomplete or latent data, the EM algorithm iteratively increases the likelihood. Profile
Relationship to Bayesian methods and model selection: in Bayesian inference, the likelihood is combined with a