Truncated Power Prior Distribution for Models

Creates an object representing the prior distribution on models for BAS using a truncated Distribution on the Model Size where the probability of gamma = p^-kappa |gamma| where gamma is the vector of model indicators

Usage

tr.power.prior(kappa = 2, trunc)

Arguments

kappa

parameter in the prior distribution that controls sparsity

trunc

parameter that determines truncation in the distribution i.e. P(gamma; alpha, beta, trunc) = 0 if |gamma| > trunc.

Value

returns an object of class "prior", with the family and hyperparameters.

Details

The beta-binomial distribution on model size is obtained by assigning each variable inclusion indicator independent Bernoulli distributions with probability w, and then giving w a beta(alpha,beta) distribution. Marginalizing over w leads to the number of included predictors having a beta-binomial distribution. The default hyperparameters lead to a uniform distribution over model size. The Truncated version assigns zero probability to all models of size > trunc.

See also

bas.lm, Bernoulli,uniform

Other priors modelpriors: Bernoulli.heredity(), Bernoulli(), beta.binomial(), tr.beta.binomial(), tr.poisson(), uniform()

Author

Merlise Clyde

Examples

tr.power.prior(2, 8)
#> $family
#> [1] "Trunc-Power-Prior"
#> 
#> $hyper.parameters
#> [1] 2 8
#> 
#> attr(,"class")
#> [1] "prior"
library(MASS)
data(UScrime)
UScrime[, -2] <- log(UScrime[, -2])
crime.bic <- bas.lm(y ~ .,
  data = UScrime, n.models = 2^15, prior = "BIC",
  modelprior = tr.power.prior(2, 8),
  initprobs = "eplogp"
)