horseshoe {brms}  R Documentation 
Regularized horseshoe priors in brms
Description
Function used to set up regularized horseshoe priors and related hierarchical shrinkage priors for populationlevel effects in brms. The function does not evaluate its arguments – it exists purely to help set up the model.
Usage
horseshoe(
df = 1,
scale_global = 1,
df_global = 1,
scale_slab = 2,
df_slab = 4,
par_ratio = NULL,
autoscale = TRUE,
main = FALSE
)
Arguments
df 
Degrees of freedom of studentt prior of the
local shrinkage parameters. Defaults to 
scale_global 
Scale of the studentt prior of the global shrinkage
parameter. Defaults to 
df_global 
Degrees of freedom of studentt prior of the
global shrinkage parameter. Defaults to 
scale_slab 
Scale of the Studentt slab. Defaults to 
df_slab 
Degrees of freedom of the studentt slab.
Defaults to 
par_ratio 
Ratio of the expected number of nonzero coefficients
to the expected number of zero coefficients. If specified,

autoscale 
Logical; indicating whether the horseshoe
prior should be scaled using the residual standard deviation

main 
Logical (defaults to 
Details
The horseshoe prior is a special shrinkage prior initially proposed by
Carvalho et al. (2009).
It is symmetric around zero with fat tails and an infinitely large spike
at zero. This makes it ideal for sparse models that have
many regression coefficients, although only a minority of them is nonzero.
The horseshoe prior can be applied on all populationlevel effects at once
(excluding the intercept) by using set_prior("horseshoe(1)")
.
The 1
implies that the studentt prior of the local shrinkage
parameters has 1 degrees of freedom. This may, however, lead to an
increased number of divergent transition in Stan.
Accordingly, increasing the degrees of freedom to slightly higher values
(e.g., 3
) may often be a better option, although the prior
no longer resembles a horseshoe in this case.
Further, the scale of the global shrinkage parameter plays an important role
in amount of shrinkage applied. It defaults to 1
,
but this may result in too few shrinkage (Piironen & Vehtari, 2016).
It is thus possible to change the scale using argument scale_global
of the horseshoe prior, for instance horseshoe(1, scale_global = 0.5)
.
In linear models, scale_global
will internally be multiplied by the
residual standard deviation parameter sigma
. See Piironen and
Vehtari (2016) for recommendations how to properly set the global scale.
The degrees of freedom of the global shrinkage prior may also be
adjusted via argument df_global
.
Piironen and Vehtari (2017) recommend to specifying the ratio of the
expected number of nonzero coefficients to the expected number of zero
coefficients par_ratio
rather than scale_global
directly.
As proposed by Piironen and Vehtari (2017), an additional regularization
is applied that only affects nonzero coefficients. The amount of
regularization can be controlled via scale_slab
and df_slab
.
To make sure that shrinkage can equally affect all coefficients,
predictors should be one the same scale.
Generally, models with horseshoe priors a more likely than other models
to have divergent transitions so that increasing adapt_delta
from 0.8
to values closer to 1
will often be necessary.
See the documentation of brm
for instructions
on how to increase adapt_delta
.
Currently, the following classes support the horseshoe prior: b
(overall regression coefficients), sds
(SDs of smoothing splines),
sdgp
(SDs of Gaussian processes), ar
(autoregressive
coefficients), ma
(moving average coefficients), sderr
(SD of
latent residuals), sdcar
(SD of spatial CAR structures), sd
(SD of varying coefficients).
Value
A character string obtained by match.call()
with
additional arguments.
References
Carvalho, C. M., Polson, N. G., & Scott, J. G. (2009). Handling sparsity via the horseshoe. Artificial Intelligence and Statistics. http://proceedings.mlr.press/v5/carvalho09a
Piironen J. & Vehtari A. (2017). On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior. Artificial Intelligence and Statistics. https://arxiv.org/pdf/1610.05559v1.pdf
Piironen, J., and Vehtari, A. (2017). Sparsity information and regularization in the horseshoe and other shrinkage priors. Electronic Journal of Statistics. https://arxiv.org/abs/1707.01694
See Also
Examples
set_prior(horseshoe(df = 3, par_ratio = 0.1))
# specify the horseshoe prior across multiple parameter classes
set_prior(horseshoe(df = 3, par_ratio = 0.1, main = TRUE), class = "b") +
set_prior(horseshoe(), class = "sd")