set_prior: Prior Definitions for 'brms' Models

View source: R/priors.R

set_priorR Documentation

Prior Definitions for brms Models


Define priors for specific parameters or classes of parameters.


  class = "b",
  coef = "",
  group = "",
  resp = "",
  dpar = "",
  nlpar = "",
  lb = NA,
  ub = NA,
  check = TRUE

prior(prior, ...)

prior_(prior, ...)

prior_string(prior, ...)




A character string defining a distribution in Stan language


The parameter class. Defaults to "b" (i.e. population-level effects). See 'Details' for other valid parameter classes.


Name of the coefficient within the parameter class.


Grouping factor for group-level parameters.


Name of the response variable. Only used in multivariate models.


Name of a distributional parameter. Only used in distributional models.


Name of a non-linear parameter. Only used in non-linear models.


Lower bound for parameter restriction. Currently only allowed for classes "b". Defaults to NULL, that is no restriction.


Upper bound for parameter restriction. Currently only allowed for classes "b". Defaults to NULL, that is no restriction.


Logical; Indicates whether priors should be checked for validity (as far as possible). Defaults to TRUE. If FALSE, prior is passed to the Stan code as is, and all other arguments are ignored.


Arguments passed to set_prior.


set_prior is used to define prior distributions for parameters in brms models. The functions prior, prior_, and prior_string are aliases of set_prior each allowing for a different kind of argument specification. prior allows specifying arguments as expression without quotation marks using non-standard evaluation. prior_ allows specifying arguments as one-sided formulas or wrapped in quote. prior_string allows specifying arguments as strings just as set_prior itself.

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

To combine multiple priors, use c(...) or the + operator (see 'Examples'). brms does not check if the priors are written in correct Stan language. Instead, Stan will check their syntactical correctness when the model is parsed to C++ and returns an error if they are not. This, however, does not imply that priors are always meaningful if they are accepted by Stan. Although brms trys to find common problems (e.g., setting bounded priors on unbounded parameters), there is no guarantee that the defined priors are reasonable for the model. Below, we list the types of parameters in brms models, for which the user can specify prior distributions.

Below, we provide details for the individual parameter classes that you can set priors on. 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.

1. Population-level ('fixed') effects

Every Population-level effect has its own regression parameter represents the name of the corresponding population-level 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 population-level effects (including monotonic 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 population-level effects at once, we may write as a shortcut set_prior("<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 = "x1") at the same time. This will set a normal(0, 10) prior on the effect of x1 and a normal(0, 2) prior on all other population-level effects. However, this will break vectorization and may slow down the sampling procedure a bit.

In case of the default intercept parameterization (discussed in the 'Details' section of brmsformula), general priors on class "b" will not affect the intercept. Instead, the intercept has its own parameter class named "Intercept" and priors can thus be specified via set_prior("<prior>", class = "Intercept"). Setting a prior on the intercept will not break vectorization of the other population-level effects. Note that technically, this prior is set on an intercept that results when internally centering all population-level predictors around zero to improve sampling efficiency. On this centered intercept, specifying a prior is actually much easier and intuitive than on the original intercept, since the former represents the expected response value when all predictors are at their means. To treat the intercept as an ordinary population-level effect and avoid the centering parameterization, use 0 + Intercept on the right-hand side of the model formula.

In non-linear models, population-level effects are defined separately for each non-linear parameter. Accordingly, it is necessary to specify the non-linear parameter in set_prior so that priors we can be assigned correctly. If, for instance, alpha is the parameter and x the predictor for which we want to define the prior, we can write set_prior("<prior>", coef = "x", nlpar = "alpha"). As a shortcut we can use set_prior("<prior>", nlpar = "alpha") to set the same prior on all population-level effects of alpha at once.

The same goes for specifying priors for specific distributional parameters in the context of distributional regression, for example, set_prior("<prior>", coef = "x", dpar = "sigma"). For most other parameter classes (see below), you need to indicate non-linear and distributional parameters in the same way as shown here.

If desired, population-level effects can be restricted to fall only within a certain interval using the lb and ub arguments of set_prior. This is often required when defining priors that are not defined everywhere on the real line, such as uniform or gamma priors. When defining a uniform(2,4) prior, you should write set_prior("uniform(2,4)", lb = 2, ub = 4). When using a prior that is defined on the positive reals only (such as a gamma prior) set lb = 0. In most situations, it is not useful to restrict population-level parameters through bounded priors (non-linear models are an important exception), but if you really want to this is the way to go.

2. Group-level ('random') effects

Each group-level effect of each grouping factor has a standard deviation named sd_<group>_<coef>. Consider, for instance, the formula y ~ x1 + x2 + (1 + x1 | g). We see that the intercept as well as x1 are group-level 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 restricted to be non-negative and, by default, have a half student-t prior with 3 degrees of freedom and a scale parameter that depends on the standard deviation of the response after applying the link function. Minimally, the scale parameter is 2.5. This prior is used (a) to be only weakly informative in order to influence results as few as possible, while (b) providing at least some regularization to considerably improve convergence and sampling efficiency. To define a prior distribution only for standard deviations of a specific grouping factor, use
set_prior("<prior>", class = "sd", group = "<group>"). To define a prior distribution only for a specific standard deviation of a specific grouping factor, you may write
set_prior("<prior>", class = "sd", group = "<group>", coef = "<coef>").

If there is more than one group-level effect per grouping factor, the correlations between those 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 (Cholesky 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"). Internally, the priors are transformed to be put on the Cholesky factors of the correlation matrices to improve efficiency and numerical stability. The corresponding parameter class of the Cholesky factors is L, but it is not recommended to specify priors for this parameter class directly.

4. Smoothing Splines

Smoothing splines are implemented in brms using the 'random effects' formulation as explained in gamm). Thus, each spline has its corresponding standard deviations modeling the variability within this term. In brms, this parameter class is called sds and priors can be specified via set_prior("<prior>", class = "sds", coef = "<term label>"). The default prior is the same as for standard deviations of group-level effects.

5. Gaussian processes

Gaussian processes as currently implemented in brms have two parameters, the standard deviation parameter sdgp, and characteristic length-scale parameter lscale (see gp for more details). The default prior of sdgp is the same as for standard deviations of group-level effects. The default prior of lscale is an informative inverse-gamma prior specifically tuned to the covariates of the Gaussian process (for more details see This tuned prior may be overly informative in some cases, so please consider other priors as well to make sure inference is robust to the prior specification. If tuning fails, a half-normal prior is used instead.

6. Autocorrelation parameters

The autocorrelation parameters currently implemented are named ar (autoregression), ma (moving average), sderr (standard deviation of latent residuals in latent ARMA models), cosy (compound symmetry correlation), car (spatial conditional autoregression), as well as lagsar and errorsar (spatial simultaneous autoregression).

Priors can be defined by set_prior("<prior>", class = "ar") for ar and similar for other autocorrelation parameters. By default, ar and ma are bounded between -1 and 1; cosy, car, lagsar, and errorsar are bounded between 0 and 1. The default priors are flat over the respective definition areas.

7. Parameters of measurement error terms

Latent variables induced via measurement error me terms require both mean and standard deviation parameters, whose prior classes are named "meanme" and "sdme", respectively. If multiple latent variables are induced this way, their correlation matrix will be modeled as well and corresponding priors can be specified via the "corme" class. All of the above parameters have flat priors over their respective definition spaces by default.

8. Distance parameters of monotonic effects

As explained in the details section of brm, monotonic effects make use of a special parameter vector to estimate the 'normalized distances' between consecutive predictor categories. This is realized in Stan using the simplex parameter type. This class is named "simo" (short for simplex monotonic) in brms. The only valid prior for simplex parameters is the dirichlet prior, which accepts a vector of length K - 1 (K = number of predictor categories) as input defining the 'concentration' of the distribution. Explaining the dirichlet prior is beyond the scope of this documentation, but we want to describe how to define this prior syntactically correct. If a predictor x with K categories is modeled as monotonic, we can define a prior on its corresponding simplex via
prior(dirichlet(<vector>), class = simo, coef = mox1). The 1 in the end of coef indicates that this is the first simplex in this term. If interactions between multiple monotonic variables are modeled, multiple simplexes per term are required. For <vector>, we can put in any R expression defining a vector of length K - 1. The default is a uniform prior (i.e. <vector> = rep(1, K-1)) over all simplexes of the respective dimension.

9. Parameters for specific families

Some families need additional parameters to be estimated. Families gaussian, student, skew_normal, lognormal, and gen_extreme_value need the parameter sigma to account for the residual standard deviation. By default, sigma has a half student-t prior that scales in the same way as the group-level standard deviations. Further, 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 gamma(0.01, 0.01) 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. The von_mises family needs the parameter kappa, representing the concentration parameter. By default, kappa has prior gamma(2, 0.01).

Every family specific parameter has its own prior class, so that set_prior("<prior>", class = "<parameter>") is the right way to go. All of these priors are chosen to be weakly informative, having only minimal influence on the estimations, while improving convergence and sampling efficiency.

10. Shrinkage priors

To reduce the danger of overfitting in models with many predictor terms fit on comparably sparse data, brms supports special shrinkage priors, namely the (regularized) horseshoe and the R2D2 prior. These priors can be applied on many parameter classes, either directly on the coefficient classes (e.g., class b), if directly setting priors on them is supported, or on the corresponding standard deviation hyperparameters (e.g., class sd) otherwise. Currently, the following classes support shrinkage priors: 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).

11. Fixing parameters to constants

Fixing parameters to constants is possible by using the constant function, for example, constant(1) to fix a parameter to 1. Broadcasting to vectors and matrices is done automatically.


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


  • prior(): Alias of set_prior allowing to specify arguments as expressions without quotation marks.

  • prior_(): Alias of set_prior allowing to specify arguments as as one-sided formulas or wrapped in quote.

  • prior_string(): Alias of set_prior allowing to specify arguments as strings.

  • empty_prior(): Create an empty brmsprior object.

See Also



## use alias functions
(prior1 <- prior(cauchy(0, 1), class = sd))
(prior2 <- prior_(~cauchy(0, 1), class = ~sd))
(prior3 <- prior_string("cauchy(0, 1)", class = "sd"))
identical(prior1, prior2)
identical(prior1, prior3)

# check which parameters can have priors
get_prior(rating ~ treat + period + carry + (1|subject),
          data = inhaler, family = cumulative())

# define some priors
bprior <- c(prior_string("normal(0,10)", class = "b"),
            prior(normal(1,2), class = b, coef = treat),
            prior_(~cauchy(0,2), class = ~sd,
                   group = ~subject, coef = ~Intercept))

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

# use the horseshoe prior to model sparsity in regression coefficients
make_stancode(count ~ zAge + zBase * Trt,
              data = epilepsy, family = poisson(),
              prior = set_prior("horseshoe(3)"))

# fix certain priors to constants
bprior <- prior(constant(1), class = "b") +
  prior(constant(2), class = "b", coef = "zBase") +
  prior(constant(0.5), class = "sd")
make_stancode(count ~ zAge + zBase + (1 | patient),
              data = epilepsy, prior = bprior)

# pass priors to Stan without checking
prior <- prior_string("target += normal_lpdf(b[1] | 0, 1)", check = FALSE)
make_stancode(count ~ Trt, data = epilepsy, prior = prior)

# define priors in a vectorized manner
# useful in particular for categorical or multivariate models
set_prior("normal(0, 2)", dpar = c("muX", "muY", "muZ"))

brms documentation built on Sept. 26, 2023, 1:08 a.m.