Which statement describes the dependence of the likelihood on data and parameters?

Which statement describes the dependence of the likelihood on data and parameters?

• A. Observed data only
• B. Prior information
• C. Both data and prior
• D. The sampling distribution of the estimator

Answer: (A)

The likelihood is a function of the data given the parameter values. Once you’ve observed the data, the likelihood tells you how plausible different parameter values are for those data. It depends on the observed data and on the parameter values you’re evaluating, but it does not involve prior information. In Bayesian inference, the prior enters separately and combines with the likelihood to form the posterior (posterior ∝ likelihood × prior). The sampling distribution of the estimator is about how the estimator would behave across repeated samples, not about how likely the observed data are for given parameters. So the correct description is that the likelihood depends on both the observed data and the parameter values.

The likelihood is a function of the data given the parameter values. Once you’ve observed the data, the likelihood tells you how plausible different parameter values are for those data. It depends on the observed data and on the parameter values you’re evaluating, but it does not involve prior information. In Bayesian inference, the prior enters separately and combines with the likelihood to form the posterior (posterior ∝ likelihood × prior). The sampling distribution of the estimator is about how the estimator would behave across repeated samples, not about how likely the observed data are for given parameters. So the correct description is that the likelihood depends on both the observed data and the parameter values.