AM_find_gamma_Delta {AntMAN} R Documentation

## Given that the prior on M is a dirac delta, find the γ 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 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 (Argiento and Iorio 2019). 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.

### 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
```

[Package AntMAN version 1.1.0 Index]