In Bayesian statistics, what is a prior?

In Bayesian statistics, what is a prior?

• A. The observed data
• B. The posterior distribution after observing data
• C. A distribution representing beliefs about a parameter before observing data
• D. The sampling distribution of the estimator

Answer: (C)

A prior is a distribution representing beliefs about a parameter before observing data. In Bayesian statistics, you start with what you think about the parameter, encoded as a probability distribution. This prior can reflect previous studies, theory, or be intentionally vague so the data drive the conclusion. After collecting data, you combine the prior with the likelihood (how probable the observed data are under different parameter values) to obtain the posterior distribution, which updates your beliefs in light of the data. The other options describe the observed data, the updated belief after seeing data, or the sampling behavior of a statistic, none of which capture the initial belief about the parameter before seeing data.

A prior is a distribution representing beliefs about a parameter before observing data. In Bayesian statistics, you start with what you think about the parameter, encoded as a probability distribution. This prior can reflect previous studies, theory, or be intentionally vague so the data drive the conclusion. After collecting data, you combine the prior with the likelihood (how probable the observed data are under different parameter values) to obtain the posterior distribution, which updates your beliefs in light of the data. The other options describe the observed data, the updated belief after seeing data, or the sampling behavior of a statistic, none of which capture the initial belief about the parameter before seeing data.