R Statistics Cookbook

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We have used gamma priors in order to force the beta coefficients to be greater than zero. But in STAN, we have a different option: we can put a boundary via real<lower=0> beta[6]. This is sufficient to ensure that the posterior densities are bounded by zero. Apart from this, we may or may not want to specify a prior density, which we can do, for example, using beta ~ normal(5,3). It is very important to note that, in these cases (when using the <lower> approach), that we are actually specifying improper priors, which are priors that have a density that doesn't sum up to one (a Gaussian density is defined from -∞ to ∞ and has an area of 1). But if the permissible range for this variable is now from 0 to ∞, that area-integral ...