The Likelihood Principle

The Likelihood Principle states that all the information relevant to estimating a parameter is contained in the likelihood function, which measures how compatible different parameter values are with the observed data. In simple terms, once you've seen your data, your conclusions about the parameter should depend only on how likely that data makes each possible parameter value, not on other factors like the sampling method or hypothetical data. This means the evidence provided by the data guides your inferences directly, emphasizing the importance of the observed data's fit to different parameter assumptions.