AM_find_gamma_Delta: Given that the prior on M is a dirac delta, find the gamma...
In AntMAN: Anthology of Mixture Analysis Tools

Description Usage Arguments Value Examples

Once a fixed value of the number of components M^* is specified, this function adopts a bisection method to find the value of γ 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 γ \insertCiteargiento2019infinityAntMAN. The user can provide a lower γ_{l} and an upper γ_{u} bound for the possible values of γ. The default values are γ_l= 10^{-3} and γ_{u}=10. A default value for the tolerance is ε=0.1. Moreover, after a maximum number of iteration (default is 31), the function stops warning that convergence has not been reached.

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

`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.

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

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