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In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior distribution represents a greater degree of information.

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When to stop the chain of priors in Bayesian hierarchical models?

From Wkipedia's article on hyperprior: In Bayesian statistics, a hyperprior is a prior distribution on a hyperparameter, that is, on a parameter of a prior distribution. … There will be some parameters for the hyperprior and there is nothing stopping us from defining prior distribution on these parameters too. …