AM_find_gamma_Delta function

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

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 $\gamma$ if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="argiento2019infinity",package="AntMAN",cached_env=.Rdpack.currefs) . 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.

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.

Returns

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