In Bayesian statistics, what term describes a prior distribution that narrows beliefs about a parameter to a degree?

In Bayesian statistics, what term describes a prior distribution that narrows beliefs about a parameter to a degree?

• A. Informative prior distribution
• B. Uninformative prior
• C. Noninformative prior
• D. Conjugate prior

Answer: (A)

In Bayesian analysis, the prior distribution represents what you believe about a parameter before seeing the data. When that prior narrows beliefs about the parameter to a degree—meaning it encodes specific knowledge or a strong expectation about where the parameter should lie—it’s an informative prior. Such a prior has concentrated mass or a small spread, so it exerts a noticeable influence on the posterior, especially when the data are limited or noisy. Concretely, an informative prior might reflect expert opinion or prior study results, fixing the parameter around a plausible value with relatively low uncertainty. The math shows up as a prior with smaller variance or a concentrated shape, so the posterior combines this strong prior belief with the information from the likelihood. The other terms don’t capture this narrowing effect. An uninformative (or noninformative) prior aims to be vague so the data drive the posterior, not prior beliefs. A conjugate prior is chosen for mathematical convenience because it yields a posterior in the same distribution family, but it isn’t defined by how strongly it narrows beliefs.

In Bayesian analysis, the prior distribution represents what you believe about a parameter before seeing the data. When that prior narrows beliefs about the parameter to a degree—meaning it encodes specific knowledge or a strong expectation about where the parameter should lie—it’s an informative prior. Such a prior has concentrated mass or a small spread, so it exerts a noticeable influence on the posterior, especially when the data are limited or noisy.

Concretely, an informative prior might reflect expert opinion or prior study results, fixing the parameter around a plausible value with relatively low uncertainty. The math shows up as a prior with smaller variance or a concentrated shape, so the posterior combines this strong prior belief with the information from the likelihood.

The other terms don’t capture this narrowing effect. An uninformative (or noninformative) prior aims to be vague so the data drive the posterior, not prior beliefs. A conjugate prior is chosen for mathematical convenience because it yields a posterior in the same distribution family, but it isn’t defined by how strongly it narrows beliefs.