Function used to set up a horseshoe prior for population-level effects in brms. The function does not evaluate its arguments -- it exists purely to help set up the model.

```
horseshoe(df = 1, scale_global = 1, df_global = 1, scale_slab = 2,
df_slab = 4, par_ratio = NULL, autoscale = TRUE)
```

df

Degrees of freedom of student-t prior of the
local shrinkage parameters. Defaults to `1`

.

scale_global

Scale of the student-t prior of the global shrinkage
parameter. Defaults to `1`

.
In linear models, `scale_global`

will internally be
multiplied by the residual standard deviation parameter `sigma`

.

df_global

Degrees of freedom of student-t prior of the
global shrinkage parameter. Defaults to `1`

.

scale_slab

Scale of the student-t prior of the regularization
parameter. Defaults to `2`

.

df_slab

Degrees of freedom of the student-t prior of
the regularization parameter. Defaults to `4`

.

par_ratio

Ratio of the expected number of non-zero coefficients
to the expected number of zero coefficients. If specified,
`scale_global`

is ignored and internally computed as
`par_ratio / sqrt(N)`

, where `N`

is the total number
of observations in the data.

autoscale

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

if possible and sensible (defaults to `TRUE`

).
Autoscaling is not applied for distributional parameters or
when the model does not contain the parameter `sigma`

.

A character string obtained by `match.call()`

with
additional arguments.

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 non-zero.
The horseshoe prior can be applied on all population-level effects at once
(excluding the intercept) by using `set_prior("horseshoe(1)")`

.
The `1`

implies that the student-t 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 non-zero 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 non-zero 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`

.

Carvalho, C. M., Polson, N. G., & Scott, J. G. (2009). Handling sparsity via the horseshoe. In International Conference on Artificial Intelligence and Statistics (pp. 73-80).

Piironen J. & Vehtari A. (2016). On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior. https://arxiv.org/pdf/1610.05559v1.pdf

Piironen, J., and Vehtari, A. (2017). Sparsity information and regularization in the horseshoe and other shrinkage priors. https://arxiv.org/abs/1707.01694

```
# NOT RUN {
set_prior(horseshoe(df = 3, par_ratio = 0.1))
# }
```

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