AM_find_gamma_Pois {AntMAN}

Given that the prior on M is a shifted Poisson, find the \gamma hyperparameter of the weights prior to match E(K)=K^{*}, where K^{*} is user-specified

Description

Once the prior on the number of mixture components M is assumed to be a Shifted Poisson of parameter Lambda, this function adopts a bisection method to find the value of \gamma such that the induced distribution on the number of clusters is centered around a user specifed value K^{*}, i.e. the function uses a bisection method to solve for \gamma (Argiento and Iorio 2019). The user can provide a lower \gamma_{l} and an upper \gamma_{u} bound for the possible values of \gamma. The default values are \gamma_l= 10^{-3} and \gamma_{u}=10. A defaault value for the tolerance is \epsilon=0.1. Moreover, after a maximum number of iteration (default is 31), the function stops warning that convergence has not bee reached.

Usage

AM_find_gamma_Pois(
  n,
  Lambda,
  Kstar = 6,
  gam_min = 1e-04,
  gam_max = 10,
  tolerance = 0.1
)

Arguments

n

The sample size.

Lambda

The parameter of the Shifted Poisson for the number of components of the mixture.

Kstar

The mean number of clusters the user wants to specify.

gam_min

The lower bound of the interval in which gamma should lie.

gam_max

The upper bound of the interval in which gamma should lie.

tolerance

Level of tolerance of the method.

Value

A value of gamma such that E(K)=K^{*}

Examples

n <- 82
Lam  <- 11
gam_po <-  AM_find_gamma_Pois(n,Lam,Kstar=6, gam_min=0.0001,gam_max=10, tolerance=0.1)
prior_K_po <-  AM_prior_K_Pois(n,gam_po,Lam)
prior_K_po%*%1:n