# set_prior

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##### Prior Definitions for brms Models

Define priors for specific parameters or classes of parameters

##### Usage
set_prior(prior, class = "b", coef = "", group = "")
##### Arguments
prior
A character string defining a distribution in Stan language
class
The parameter class. Defaults to "b" (fixed effects). See 'Details' for other valid parameter classes.
coef
Name of the (fixed, category specific, or random effects) parameter
group
Grouping factor for random effects parameters.
##### Details

set_prior is used to define prior distributions for parameters in brms models. Below, we explain its usage and list some common prior distributions for parameters. A complete overview on possible prior distributions is given in the Stan Reference Manual available at http://mc-stan.org/. To combine multiple priors, use c(...), e.g., c(set_prior(...), set_prior(...)). brms performs no checks if the priors are written in correct Stan language. Instead, Stan will check their correctness when the model is parsed to C++ and returns an error if they are not. Currently, there are five types of parameters in brms models, for which the user can specify prior distributions. 1. Fixed and category specific effects Every fixed (and category specific) effect has its own regression parameter. These parameters are internally named as b_, where represents the name of the corresponding fixed effect. Suppose, for instance, that y is predicted by x1 and x2 (i.e. y ~ x1+x2 in formula syntax). Then, x1 and x2 have regression parameters b_x1 and b_x2 respectively. The default prior for fixed and category specific effects is an improper flat prior over the reals. Other common options are normal priors or student-t priors. If we want to have a normal prior with mean 0 and standard deviation 5 for x1, and a unit student-t prior with 10 degrees of freedom for x2, we can specify this via set_prior("normal(0,5)", class = "b", coef = "x1") and set_prior("student_t(10,0,1)", class = "b", coef = "x2"). To put the same prior on all fixed effects at once, we may write as a shortcut set_prior("", class = "b"). This also leads to faster sampling, because priors can be vectorized in this case. Both ways of defining priors can be combined using for instance set_prior("normal(0,2)", class = "b") and set_prior("normal(0,10)", class = "b", coef = "Intercept") at the same time. This will set a normal(0,10) prior on the Intercept and a normal(0,2) prior on all other fixed effects. The intercept can have a separate prior without breaking vectorization. However, this is not the case for other fixed effects. A special shrinkage prior to be applied on fixed effects is the horseshoe prior. 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. For more details see Carvalho et al. (2009). The horseshoe prior can be applied on all fixed effects at once (excluding the intercept) by using set_prior("horseshoe()"). Replace with the desired degrees of freedom of the student-t prior of the local shrinkage parameters. In their paper, Carvalho et al. (2009) use one degrees of freedom, but this my lead to an increased number of divergent transition in Stan so that slightly higher values may often be a better option. 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. 3. Autocorrelation parameters The autocorrelation parameters currently implemented are named ar (autoregression), ma (moving average), and arr (autoregression of the response). The default prior for autocorrelation parameters is an improper flat prior over the reals. Other priors can be defined by set_prior("", class = "ar") for ar effects and similar for ma and arr effects. 4. Standard deviations of random effects Each random effect of each grouping factor has a standard deviation named sd__. Consider, for instance, the formula y ~ x1+x2+(1+x1|g). We see that the intercept as well as x1 are random effects nested in the grouping factor g. The corresponding standard deviation parameters are named as sd_g_Intercept and sd_g_x1 respectively. These parameters are restriced to be non-negative and, by default, have a half cauchy prior with a scale parameter that depends on the standard deviation of the response after applying the link function. Minimally, the scale parameter is 5. To define a prior distribution only for standard deviations of a specific grouping factor, use set_prior("", class = "sd", group = ""). To define a prior distribution only for a specific standard deviation of a specific grouping factor, you may write set_prior("", class = "sd", group = "", coef = ""). Recommendations on useful prior distributions for standard deviations are given in Gelman (2006). 5. Correlations of random effects If there is more than one random effect per grouping factor, the correlations between those random effects have to be estimated. The prior "lkj_corr_cholesky(eta)" or in short "lkj(eta)" with eta > 0 is essentially the only prior for (choelsky factors) of correlation matrices. If eta = 1 (the default) all correlations matrices are equally likely a priori. If eta > 1, extreme correlations become less likely, whereas 0 < eta < 1 results in higher probabilities for extreme correlations. Correlation matrix parameters in brms models are named as cor_(group), (e.g., cor_g if g is the grouping factor). To set the same prior on every correlation matrix, use for instance set_prior("lkj(2)", class = "cor"). 6. Parameters for specific families Some families need additional parameters to be estimated. Families gaussian, student, and cauchy need the parameter sigma to account for the residual standard deviation. By default, sigma has a half cauchy prior that scales in the same way as the random effects standard deviations. Furthermore, family student needs the parameter nu representing the degrees of freedom of students t distribution. By default, nu has prior "gamma(2,0.1)" and a fixed lower bound of 1. Families gamma, weibull, inverse.gaussian, and negbinomial need a shape parameter that has a "cauchy(0,5)" prior by default. For families cumulative, cratio, sratio, and acat, and only if threshold = "equidistant", the parameter delta is used to model the distance between two adjacent thresholds. By default, delta has an improper flat prior over the reals. Every family specific parameter has its own prior class, so that set_prior("", class = "") it the right way to go. Often, it may not be immediately clear, which parameters are present in the model. To get a full list of parameters and parameter classes for which priors can be specified (depending on the model) use function get_prior.

##### Value

• An object of class brmsprior to be used in the prior argument of brm.

##### References

Gelman A (2006). Prior distributions for variance parameters in hierarchical models. Bayesian analysis, 1(3), 515 -- 534. 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).

get_prior

• set_prior
##### Examples
## check which parameters can have priors
get_prior(rating ~ treat + period + carry + (1|subject),
data = inhaler, family = sratio(),
threshold = "equidistant")

## define some priors
prior <- c(set_prior("normal(0,10)", class = "b"),
set_prior("normal(1,2)", class = "b", coef = "treat"),
set_prior("cauchy(0,2)", class = "sd",
group = "subject", coef = "Intercept"),
set_prior("uniform(-5,5)", class = "delta"))

## verify that the priors indeed found their way into Stan's model code
make_stancode(rating ~ period + carry + (1|subject),
data = inhaler, family = sratio(),
partial = ~ treat, threshold = "equidistant",
prior = prior)

## use horseshoe priors to model sparsity in fixed effects parameters
make_stancode(count ~ log_Age_c + log_Base4_c * Trt_c,
data = epilepsy, family = poisson(),
prior = set_prior("horseshoe(3)"))
Documentation reproduced from package brms, version 0.7.0, License: GPL (>= 3)

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