Places a distribution on g(x) rather than directly on the declared model
parameter x, where g is a package-defined transformation. The Stan
density includes the log absolute Jacobian of g. The same scalar
distribution is applied independently to each component of a vector.
Arguments
- dist
(
Prior) a scalar distribution prior: normal, standard normal, Cauchy, gamma, log-normal, beta, uniform, Student-t, logistic, log-logistic or inverse-gamma. Constant, flat, initialization-only, vector-specific, horseshoe and already transformed priors are not supported.- transform
(
PriorTransform) package-defined transformation from the model parameter to the prior density scale, created byprior_transform_exp()orprior_transform_square().
Details
Equivalently, supply transform directly to a scalar distribution helper.
The density is proportional to p(g(x)) * abs(g'(x)). Distribution support
and any existing limits on dist are intersected with the transformation's
range and mapped back to bounds on x. Subsequent set_limits() calls use
the model parameter scale and retain these support restrictions. Truncation
normalisation is evaluated on the density scale.
Initial values are drawn on the density scale within the mapped bounds,
inverse-transformed and shrunk towards a centre on the model parameter
scale using jmpost.prior_shrinkage. If the inverse-transformed distribution
centre is outside the bounds or non-finite, an interior reference value is
used. Initialization uses bounded rejection sampling and reports an error
when the admissible region has too little probability to find valid draws.
This changes the prior distribution. Predictor parametrizations and Stan affine multipliers serve different purposes and do not supply this Jacobian.
Slots
distribution(
Prior)
Distribution on the transformed scale.transform(
PriorTransform)
Transformation to the density scale.
See also
Other Prior:
prior_beta(),
prior_cauchy(),
prior_const(),
prior_const_vector(),
prior_flat(),
prior_gamma(),
prior_horseshoe(),
prior_init_only(),
prior_invgamma(),
prior_logistic(),
prior_loglogistic(),
prior_lognormal(),
prior_normal(),
prior_normal_vector(),
prior_std_normal(),
prior_student_t(),
prior_uniform()
Examples
prior_normal(60, 60, transform = prior_transform_exp())
#>
#> Prior Object:
#> normal(mu = 60, sigma = 60) T[0, ] on exp(x)
#>
prior_invgamma(1.5, 0.3, transform = prior_transform_exp(scale = 2))
#>
#> Prior Object:
#> inv_gamma(alpha = 1.5, beta = 0.3) on exp(2 * (x))
#>
prior_transform(prior_normal(100, 100), prior_transform_square())
#>
#> Prior Object:
#> normal(mu = 100, sigma = 100) T[0, ] on square(x); x T[0, ]
#>