Named prior families

Priors built from a named distribution family, one marginal per parameter, following Stan's argument names and argument order. Each constructor is vectorized: pass a vector where Stan would write one sampling statement per component, and pass a scalar to use the same value for every parameter. Naming any of the vectors (e.g. c(beta = 2, gamma = 3)) names the parameters, exactly as naming low does in prior_uniform().

Usage

prior_lognormal(meanlog = 0, sdlog = 1)

prior_exponential(rate = 1)

prior_gamma(shape, rate = 1)

prior_beta(shape1, shape2)

prior_student_t(df, location = 0, scale = 1)

prior_cauchy(location = 0, scale = 1)

prior_half_normal(sd = 1)

prior_half_cauchy(scale = 1)

Arguments

meanlog, sdlog

Log-scale mean and standard deviation of the log-normal, as in stats::dlnorm() and Stan's lognormal.

rate

Rate of the exponential or gamma, as in stats::dexp() and Stan's exponential/gamma. Must be positive.

shape

Shape of the gamma. Must be positive.

shape1, shape2

Beta shape parameters, as in stats::dbeta(). Both must be positive.

df

Degrees of freedom of the Student-t. Must be positive.

location, scale

Location and scale of the Student-t, the Cauchy or the half-Cauchy. scale must be positive.

sd

Standard deviation of the normal underlying the half-normal. Must be positive.

Value

An nsbi_prior object.

Details

Families with constrained support set lower/upper on the prior, so the posterior's leakage correction (see posterior()) rejects and renormalizes against the right region without any further declaration. A gamma prior bounds at zero, a beta prior at zero and one, and the half families at zero.

A prior built here can be truncated further with prior_truncated(), combined with others through prior_independent(), and written out by stan_code() as the sampling statement it came from. That is the reason these exist as families rather than as recipes for prior_custom(): the family is what carries over to Stan and to the truncation constant.

prior_half_normal() and prior_half_cauchy() are the zero-centred families truncated to \([0, \infty)\), matching Stan's idiom of declaring real<lower=0> and writing sigma ~ normal(0, 1). Their densities carry the log(2) renormalization, which Stan drops as a constant and this package cannot. For a half-normal centred somewhere other than zero, wrap prior_normal() in prior_truncated().

See also

prior_independent() to combine several of these into one joint prior, prior_truncated() to bound one, and priors for the rest.

Examples

# One log-normal per parameter, named through the vector.
prior <- prior_lognormal(meanlog = c(beta = log(0.4), gamma = log(0.125)),
                         sdlog = c(0.5, 0.2))
theta <- sample_prior(prior, 5)

# A scalar argument is shared: three gammas with the same rate.
prior_gamma(shape = c(2, 5, 9), rate = 3)
#> <nsbi_prior> type=gamma, dim=3
#>   lower: 0, 0, 0 
#>   theta[1] ~ gamma(2, 3)
#>   theta[2] ~ gamma(5, 3)
#>   theta[3] ~ gamma(9, 3)

# Support bounds come from the family, and drive the leakage correction.
# A bare vector is read as a single row, so several 1-d draws need an
# explicit column matrix.
within_support(prior_beta(2, 15), matrix(c(0.1, 1.5), ncol = 1))
#> [1]  TRUE FALSE