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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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Parameters without defined priors in Stan

From the Stan reference v1.0.2 (pg 6, footnote 1) If no prior were specified in the model block, the constraints on theta ensure it falls between 0 and 1, providing theta an implicit uniform prior. … For parameters with no prior specified and unbounded support, the result is an improper prior. Stan accepts improper priors, but posteriors must be proper in order for sampling to succeed. …
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