AM_find_gamma_Delta {AntMAN}

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 (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 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

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