AM_mix_components_prior_negbin: Generate a configuration object for a Shifted Negative Binomial prior on the number of mixture components

Description

This generates a configuration object for a Shifted Negative Binomial prior on the number of mixture components such that $$q_M(m)=Pr(M=m) =\frac{\Gamma(r+m-1)}{(m-1)!\Gamma(r)} p^{m-1}(1-p)^r, \quad m=1,2,3,\ldots$$ The hyperparameters $p\in (0,1)$ (probability of success) and $r>0$ (size) can either be fixed using r and p or assigned appropriate prior distributions. In the latter case, we assume $p \sim Beta(a_P,b_P)$ and $r \sim Gamma(a_R,b_R)$. In AntMAN we assume the following parametrization of the Gamma density: $$p(x\mid a,b )= \frac{b^a x^{a-1}}{\Gamma(a)} \exp\{ -bx \}, \quad x>0.$$

Usage

AM_mix_components_prior_negbin(
  a_R = NULL,
  b_R = NULL,
  a_P = NULL,
  b_P = NULL,
  R = NULL,
  P = NULL,
  init_R = NULL,
  init_P = NULL
)

Arguments

a_R

The shape parameter $a$ of the $Gamma(a,b)$ prior distribution for $r$.

b_R

The rate parameter $b$ of the $Gamma(a,b)$ prior distribution for $r$.

a_P

The parameter $a$ of the $Beta(a,b)$ prior distribution for $p$.

b_P

The parameter $b$ of the $Beta(a,b)$ prior distribution for $p$.

It allows to fix $r$ to a specific value.

It allows to fix $p$ to a specific value.

init_R

The initial value of $r$, when specifying a_R and b_R.

init_P

The inivial value of $p$, when specifying a_P and b_P.

Value

An AM_mix_components_prior object. This is a configuration list to be used as mix_components_prior argument for AM_mcmc_fit.

Details

If no arguments are provided, the default is $r = 1 , a_P = 1, b_P = 1$.

Additionally, when init_R and init_P are not specified, there are default values: $init_R = 1$ and $init_P = 0.5$.

Examples

Run this code

# NOT RUN {
AM_mix_components_prior_negbin (R=1, P=1)
AM_mix_components_prior_negbin ()
# }