For any fixed and random effect INLA supports a range of different priors of exponential distributions.

Currently supported for INLA in ibis.iSDM are the following priors that can
be specified via `"type"`

:

`"normal"`

or`"gaussian"`

: Priors on normal distributed and set to specified variable. Required parameters are a mean and a precision estimate provided to`"hyper"`

. Note that precision is not equivalent (rather the inverse) to typical standard deviation specified in Gaussian priors. Defaults are set to a mean of`0`

and a precision of`0.001`

.`"clinear"`

: Prior that places a constraint on the linear coefficients of a model so as that the coefficient is in a specified interval`"c(lower,upper)"`

. Specified through hyper these values can be negative, positive or infinite.`"spde"`

, specifically`'prior.range'`

and`'prior.sigma'`

: Specification of penalized complexity priors which can be added to a SPDE spatial random effect added via`add_latent_spatial()`

. Here the range of the penalized complexity prior can be specified through`'prior.range'`

and the uncertainty via`'prior.sigma'`

both supplied to the options 'type' and 'hyper'.

Other priors available in INLA ` names(INLA::inla.models()$prior) ) `

might also work, but have not been tested!

## Usage

```
INLAPrior(variable, type = "normal", hyper = c(0, 0.001), ...)
# S4 method for character,character,ANY
INLAPrior(variable,type,hyper,...)
```

## Arguments

- variable
A

`character`

matched against existing predictors or latent effects.- type
A

`character`

specifying the type of prior to be set.- hyper
A

`vector`

with`numeric`

values to be used as hyper-parameters. See description. The default values are set to a mean of`0`

and a precision of`0.001`

.- ...
Variables passed on to prior object.

## Note

Compared to other engines, INLA does unfortunately does not support
priors related to more stringent parameter regularization such as Laplace or
Horseshoe priors, which limits the capability of `engine_inla`

for
regularization. That being said many of the default uninformative priors act
already regularize the coefficients to some degree.

## References

Rue, H., Riebler, A., Sørbye, S. H., Illian, J. B., Simpson, D. P., & Lindgren, F. K. (2017). Bayesian computing with INLA: a review. Annual Review of Statistics and Its Application, 4, 395-421.

Simpson, D., Rue, H., Riebler, A., Martins, T. G., & Sørbye, S. H. (2017). Penalising model component complexity: A principled, practical approach to constructing priors. Statistical science, 32(1), 1-28.

## See also

Other prior:
`BARTPriors()`

,
`BARTPrior()`

,
`BREGPriors()`

,
`BREGPrior()`

,
`GDBPriors()`

,
`GDBPrior()`

,
`GLMNETPriors()`

,
`GLMNETPrior()`

,
`INLAPriors()`

,
`STANPriors()`

,
`STANPrior()`

,
`XGBPriors()`

,
`XGBPrior()`

,
`add_priors()`

,
`get_priors()`

,
`priors()`

,
`rm_priors()`