Read and set the likelihood distribution corresponding to the conjugate prior distribution.
Usage
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)
#> [1] "poisson"
ess(gmix)
#> [1] 7.159378
# set conjugate partner
likelihood(gmix) <- "exp"
# ... which changes the interpretation of the mixture
ess(gmix)
#> [1] 34.93388