Likelihood Foundations and Sufficient Statistics

Define the log-likelihood function and its role in Maximum Likelihood Estimation.

State the Neyman-Fisher factorization theorem for identifying sufficient statistics.

Apply the factorization theorem to find a sufficient statistic for a parameter of a common distribution (e.g., Bernoulli or Poisson).

Interpret a sufficient statistic as a complete summary of the evidence in the data for the parameter.

State the Likelihood Principle and describe its implications for statistical inference.