R: Truncated Power Prior Distribution for Models

tr.power.prior {BAS} | R Documentation

## Truncated Power Prior Distribution for Models

### Description

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.

### 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.

### Value

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

### Author(s)

Merlise Clyde

### See Also

`bas.lm`, `Bernoulli`,`uniform`

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

### Examples

    tr.power.prior(2, 8)
    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"
    )

[Package BAS version 1.5.5 Index]