AntMAN (version 1.1.0)

AM_find_gamma_Pois: 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 \(\gamma\) argiento2019infinityAntMAN. 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

# NOT RUN {
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
# }