informative prior
"In Bayesian inference, a prior probability density function that reflects positive empirical or theoretical information regarding the value of an unknown parameter.
The contrary case, where little or no information about the parameter is available, is represented by means of a diffuse prior, alternatively known as a vague prior."
Marriott (1990)
"Informative prior: A term used in the context of Bayesian inference to indicate a prior distribution that reflects empirical or theoretical information regarding the value of an unknown parameter."
Everitt (1998)