dbetabinom: Beta-binomial probability density

In rmcelreath/rethinking: Statistical Rethinking book package

Beta-binomial probability density

Description

Functions for computing density and producing random samples from a beta-binomial probability distribution.

Usage

dbetabinom( x , size , prob , theta , shape1 , shape2 , log=FALSE )
rbetabinom( n , size , prob , theta , shape1 , shape2 )

Arguments

x	Integer values to compute probabilies of
size	Number of trials
prob	Average probability of beta distribution
theta	Dispersion of beta distribution
shape1	First shape parameter of beta distribution (alpha)
shape2	Second shape parameter of beta distribution (beta)
log	If TRUE, returns log-probability instead of probability
n	Number of random observations to sample

Details

These functions provide density and random number calculations for beta-binomial observations. The dbetabinom code is based on Ben Bolker's original code in the emdbook package.

Either prob and theta OR shape1 and shape2 must be provided. The two parameterizations are related by shape1 = prob * theta, shape2 = (1-prob) * theta.

The rbetabinom function generates random beta-binomial observations by using both rbeta and rbinom. It draws n values from a beta distribution. Then for each, it generates a random binomial observation.

Author(s)

Richard McElreath

Examples

## Not run: 
data(reedfrogs)
reedfrogs$pred_yes <- ifelse( reedfrogs$pred=="pred" , 1 , 0 )

# map model fit
# note exp(log_theta) to constrain theta to positive reals
m <- map(
    alist(
        surv ~ dbetabinom( density , p , exp(log_theta) ),
        logit(p) <- a + b*pred_yes,
        a ~ dnorm(0,10),
        b ~ dnorm(0,1),
        log_theta ~ dnorm(1,10)
    ),
    data=reedfrogs )

# map2stan model fit
# constraint on theta is passed via contraints list
m.stan <- map2stan(
    alist(
        surv ~ dbetabinom( density , p , theta ),
        logit(p) <- a + b*pred_yes,
        a ~ dnorm(0,10),
        b ~ dnorm(0,1),
        theta ~ dcauchy(0,1)
    ),
    data=reedfrogs,
    constraints=list(theta="lower=0") )

## End(Not run)

rmcelreath/rethinking documentation built on Sept. 18, 2023, 2:01 p.m.