Regularized Horseshoe Prior for a Vector Distribution

Unbounded coefficients use a non-centred parameterization through Stan's affine multiplier transform. By default, standard-normal coefficients are multiplied by the regularized horseshoe scales. A finite scale_noncentred instead uses partial non-centring, limiting the multiplier to that scale. This can reduce dependence between strongly identified coefficients and their prior scales. It changes the sampling coordinates, not the prior. The coefficient names and initial-value interface are unchanged. Coefficients with finite bounds retain a centred parameterization because Stan does not allow bounds and affine multipliers on the same declaration.

Usage

prior_horseshoe(
  df = 1,
  df_global = 1,
  df_slab = 4,
  scale_global = 1,
  scale_slab = 2,
  scale_noncentred = Inf
)

Arguments

df

(number) degrees of freedom of the half-Student-t prior for local shrinkage parameters.

df_global

(number) degrees of freedom of the half-Student-t prior for the global shrinkage parameter.

df_slab

(number) degrees of freedom of the Student-t slab.

scale_global

(number) scale of the half-Student-t prior for the global shrinkage parameter.

scale_slab

(number) scale of the Student-t slab.

scale_noncentred

(number) positive computational scale for partial non-centring, in coefficient units. If the horseshoe standard deviation is s, the multiplier is s / sqrt(1 + (s / scale_noncentred)^2). The default Inf gives full non-centring with multiplier s. This argument does not change the horseshoe hyperparameters or the prior distribution.

Value

A Prior object.

See also

Other Prior: prior_beta(), prior_cauchy(), prior_const(), prior_const_vector(), prior_flat(), prior_gamma(), prior_init_only(), prior_invgamma(), prior_logistic(), prior_loglogistic(), prior_lognormal(), prior_normal(), prior_normal_vector(), prior_std_normal(), prior_student_t(), prior_transform(), prior_uniform()

Examples

prior_horseshoe(df = 1, df_global = 1, df_slab = 4, scale_global = 0.1, scale_slab = 2)
#> 
#> Prior Object:
#>    horseshoe(df = 1, df_global = 1, df_slab = 4, scale_global = 0.1, scale_slab = 2)
#>