AM_find_gamma_Pois {AntMAN} R Documentation

## Given that the prior on M is a shifted Poisson, find the γ hyperparameter of the weights prior to match E(K)=K^{*}, where K^{*} is user-specified

### Description

Once the prior on the number of mixture components M is assumed to be a Shifted Poisson of parameter `Lambda`, 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 defaault 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 bee reached.

### Usage

```AM_find_gamma_Pois(
n,
Lambda,
Kstar = 6,
gam_min = 1e-04,
gam_max = 10,
tolerance = 0.1
)
```

### Arguments

 `n` The sample size. `Lambda` The parameter of the Shifted Poisson for the number of components of the mixture. `Kstar` The mean number of clusters the user wants to specify. `gam_min` The lower bound of the interval in which `gamma` should lie. `gam_max` The upper bound of the interval in which `gamma` should lie. `tolerance` Level of tolerance of the method.

### Value

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

### Examples

```n <- 82
Lam  <- 11
gam_po <-  AM_find_gamma_Pois(n,Lam,Kstar=6, gam_min=0.0001,gam_max=10, tolerance=0.1)
prior_K_po <-  AM_prior_K_Pois(n,gam_po,Lam)
prior_K_po%*%1:n
```

[Package AntMAN version 1.1.0 Index]