A Strong prior is a preceding assumption, theory, concept or idea upon which a current assumption, theory, concept or idea is founded.

In Bayesian statistics

Bayesian statistics

Bayesian statistics is that subset of the entire field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities...

, the term is used to contrast the case of a weak or uniformative prior probability

Prior probability

In Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p is the probability distribution that would express one's uncertainty about p before the "data"...

. A strong prior would be a type of informative prior in which the information contained in the prior distribution dominates the information contained in the data being analysed. The Bayesian analysis combines the information contained in the prior with that extracted from the data to produce the posterior distribution which, in the case of a "strong prior", would be little changed from the prior distribution.