likelihood function

Read and Set Likelihood to the Corresponding Conjugate Prior

Read and set the likelihood distribution corresponding to the conjugate prior distribution.

likelihood(mix)

likelihood(mix) <- value

Arguments

• mix: Prior mixture distribution.
• value: New likelihood. Should only be changed for Gamma priors as these are supported with either Poisson (value="poisson") or Exponential (value="exp") likelihoods.

Details

If the prior and posterior distributions are in the same family, then the prior distribution is called a conjugate prior for the likelihood function.

Supported Conjugate Prior-Likelihood Pairs

Prior/Posterior	Likelihood	Predictive	Summaries
Beta	Binomial	Beta-Binomial	n , r
Normal	Normal ( fixed $\sigma$ )	Normal	n , m , se
Gamma	Poisson	Gamma-Poisson	n , m
Gamma	Exponential	Gamma-Exp ( not supported )	n , m

Examples

# Gamma mixture
gmix <- mixgamma(c(0.3, 20, 4), c(0.7, 50, 10))

# read out conjugate partner
likelihood(gmix)

ess(gmix)

# set conjugate partner
likelihood(gmix) <- "exp"

# ... which changes the interpretation of the mixture
ess(gmix)