AM_mix_components_prior_negbin {AntMAN} R Documentation

## 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

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}}{Γ(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. R It allows to fix r to a specific value. P 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.

### 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.

### Value

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

AM_mcmc_fit