AntMAN (version 1.1.0)

AM_find_gamma_Delta: Given that the prior on M is a dirac delta, find the \(\gamma\) hyperparameter of the weights prior to match \(E(K)=K*\), where \(K*\) is user-specified

Description

Once a fixed value of the number of components \(M^*\) is specified, 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 default 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 been reached.

Usage

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

Arguments

n

sample size.

Mstar

number of components of the mixture.

Kstar

mean number of clusters the user wants to specify.

gam_min

lower bound of the interval in which gamma should lie (default 1e-4).

gam_max

upper bound of the interval in which gamma should lie (default 10).

tolerance

Level of tolerance for the method.

Value

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

Examples

# NOT RUN {
n <- 82
Mstar <- 12
gam_de <- AM_find_gamma_Delta(n,Mstar,Kstar=6, gam_min=1e-4,gam_max=10, tolerance=0.1)
prior_K_de <-  AM_prior_K_Delta(n,gam_de,Mstar)
prior_K_de%*%1:n
# }