# AM_mix_components_prior_pois: Generate a configuration object for a Poisson prior on the... In AntMAN: Anthology of Mixture Analysis Tools

## Description

This function generates a configuration object for a Shifted Poisson prior on the number of mixture components such that

q_M(m)= Pr (M=m)= \frac{e^{-Λ}Λ^{m-1} }{(m-1)!} , \quad m=1,2,3,…

The hyperparameter Λ can either be fixed using Lambda or assigned a Gamma(a,b) prior distribution with a and b. 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

 1 AM_mix_components_prior_pois(a = NULL, b = NULL, Lambda = NULL, init = NULL) 

## Arguments

 a The shape parameter a of the Gamma(a,b) prior distribution. b The rate parameter b of the Gamma(a,b) prior distribution. Lambda It allows to set the hyperparameter Λ to be assigned a fixed value. init The initial value for Λ, when specifying a and b.

## Details

If no arguments are provided, the default is a prior distribution with a = 1 and b = 1.

## 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
 1 components_prior = AM_mix_components_prior_pois (init=3, a=1, b=1)