Creates a prior distribution

prior creates a prior distribution. The prior can be visualized by the plot function.

prior(
  distribution,
  parameters,
  truncation = list(lower = -Inf, upper = Inf),
  prior_weights = 1
)

prior_none(prior_weights = 1)

Arguments

distribution

name of the prior distribution. The possible options are

"point"

for a point density characterized by a location parameter.

"normal"

for a normal distribution characterized by a mean and sd parameters.

"lognormal"

for a lognormal distribution characterized by a meanlog and sdlog parameters.

"cauchy"

for a Cauchy distribution characterized by a location and scale parameters. Internally converted into a generalized t-distribution with df = 1.

"t"

for a generalized t-distribution characterized by a location, scale, and df parameters.

"gamma"

for a gamma distribution characterized by either shape and rate, or shape and scale parameters. The latter is internally converted to the shape and rate parametrization

"invgamma"

for an inverse-gamma distribution characterized by a shape and scale parameters. The JAGS part uses the BayesTools module distribution dbt_invgamma(shape, scale) on the natural parameter.

"beta"

for a beta distribution characterized by an alpha and beta parameters.

"exp"

for an exponential distribution characterized by either rate or scale parameter. The later is internally converted to rate.

"uniform"

for a uniform distribution defined on a range from a to b

"moment"

for a Johnson-Rossell moment prior characterized by exactly one of mode or tau, an optional order that defaults to 1, and an optional location that defaults to 0.

"invmoment"

for a Johnson-Rossell inverse-moment prior characterized by exactly one of mode or tau, a df, an optional order that defaults to 1, and an optional location that defaults to 0.

"dirichlet"

for a Dirichlet distribution over a simplex, whose finite nonnegative coordinates must have a finite total and roundoff bound and sum to one within that bound, characterized by a concentration vector alpha. Numeric entries must be finite and at least 0.01; this is a supported-input minimum, not a numerical guarantee. Positive expression-valued concentrations retain their existing JAGS-only support: expression containers, including literal elements, are not statically evaluated or validated, and R random generation refuses them. Cumulative weight functions and ordered allocations require numeric concentrations. Accepted sampling can still be unavailable; see prior_functions. Two-bin cumulative JAGS initialization near the minimum can repeatedly refuse unrepresentable interior ratios. Density and plot methods show one beta marginal per simplex coordinate.

parameters

list of appropriate parameters for a given distribution.

truncation

list with two elements, lower and upper, that define the lower and upper truncation of the distribution. Defaults to list(lower = -Inf, upper = Inf). The truncation is automatically set to the bounds of the support.

prior_weights

prior odds associated with a given distribution. The value is passed into the model fitting function, which creates models corresponding to all combinations of prior distributions for each of the model parameters and sets the model priors odds to the product of its prior distributions.

Value

prior and prior_none return an object of class 'prior'. A named list containing the distribution name, parameters, and prior weights.

Details

Moment and inverse-moment priors are symmetric nonlocal priors with zero density at location. The mode parameter is the positive distance from location to each symmetric mode; supplied negative values are converted to their absolute value. Positional parameters are interpreted as mode for "moment" and mode, df for "invmoment". Use named parameters for tau, order, location, or the inverse-moment nu alias. Positional input always treats the first parameter as mode. For moment priors, tau = mode^2 / (2 * order). For inverse-moment priors, tau = mode^2 * ((df + 1) / (2 * order))^(1 / order). Aliases "pmom", "pimom", and "inversemoment" are accepted, and inverse-moment df may also be supplied as nu.

Native inverse-gamma, moment and inverse-moment calculations distinguish certified finite-input tails outside logarithmic range from unavailable arithmetic. Direct density and log-density evaluations signal BayesTools_numerical_range_limit; unresolved calculations signal BayesTools_numerical_unavailable. Both inherit BayesTools_numerical_condition and retain the original input indices, operation, family and requested scale. Truncated evaluations warn only for points inside the declared support and truncation. Numerical tail zeros do not declare zero probability mass or point atoms. Nonempty intervals whose two endpoints both lose tail-log range can have unavailable normalization. Finite-required fitting and bridge consumers refuse these range results; natural integration may consume certified negative-infinite log tails only after checking normalization and the required kernel and Jacobian. Certification requires the inspected MinGW-w64 11.x x86-64 log backend, documented Intel or AMD instruction contracts, checked floating-point modes and a checked extended logarithmic constant. Other backends, overflowing original nonlocal distances and uncertified coordinates remain unavailable in this FAR regime. Constructor parameter domains and ordinary arithmetic are unchanged.

See also

plot.prior(), Normal, Lognormal, Cauchy, Beta, Exponential, LocationScaleT, InvGamma.

Examples

# create a standard normal prior distribution
p1 <- prior(distribution = "normal", parameters = list(mean = 1, sd = 1))

# create a half-normal standard normal prior distribution
p2 <- prior(distribution = "normal", parameters = list(mean = 1, sd = 1),
truncation = list(lower = 0, upper = Inf))

# the prior distribution can be visualized using the plot function
# (see ?plot.prior for all options)
plot(p1)


# create nonlocal priors centered on zero
p3 <- prior("moment", list(mode = 0.5))
p4 <- prior("invmoment", list(mode = 0.5, df = 3))

# tau can be specified directly when named
p5 <- prior("pmom", list(tau = 0.125))
p6 <- prior("pimom", list(tau = 0.5, nu = 3))