# tr.beta.binomial: Truncated Beta-Binomial Prior Distribution for Models In BAS: Bayesian Variable Selection and Model Averaging using Bayesian Adaptive Sampling

## Description

Creates an object representing the prior distribution on models for BAS using a truncated Beta-Binomial Distribution on the Model Size

## Usage

 `1` ```tr.beta.binomial(alpha = 1, beta = 1, trunc) ```

## Arguments

 `alpha` parameter in the beta prior distribution `beta` parameter in the beta prior distribution `trunc` parameter that determines truncation in the distribution i.e. P(M; alpha, beta, trunc) = 0 if M > 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 distribution on the number of included predictos 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 hyerparameters.

## Author(s)

Merlise Clyde

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

Other priors modelpriors: `Bernoulli.heredity`, `Bernoulli`, `beta.binomial`, `tr.poisson`, `tr.power.prior`, `uniform`

## Examples

 ```1 2 3 4 5 6 7``` ```tr.beta.binomial(1,10, 5) library(MASS) data(UScrime) UScrime[,-2] = log(UScrime[,-2]) crime.bic = bas.lm(y ~ ., data=UScrime, n.models=2^15, prior="BIC", modelprior=tr.beta.binomial(1,1,8), initprobs= "eplogp") ```

BAS documentation built on Nov. 17, 2017, 4:51 a.m.