# rpg: Polya-Gamma Random Variates In BayesLogit: PolyaGamma Sampling

## Description

Generate random variates from the Polya-Gamma distribution.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```rpg(num=1, h=1, z=0.0) rpg.gamma(num=1, h=1, z=0.0, trunc=200) rpg.devroye(num=1, h=1, z=0.0) rpg.sp(num=1, h=1, z=0.0) rpg.gamma.R(num=1, h=1, z=0.0, trunc=200) rpg.devroye.R(num=1, h=1, z=0.0) ```

## Arguments

 `num` The number of random variates to simulate. `h` Shape parameter. `h` must be >= 1 if not using sum of gammas method. `z` Parameter associated with tilting. `trunc` The number of elements used in sum of gammas approximation.

## Details

A random variable X with distribution PG(h,z) is distributed like

X \sim ∑_{k=1}^∞ G(h,1) / ( 2 π^2 (k-1/2)^2 + z^2/2).

The density for X may be derived by exponentially tilting the PG(h,0) density:

p(x|h,z) \propto \exp(-x z^2/2) p(x|h,0).

Different methods for generating this random variable are implemented, each of which is useful for certain parameters. The parameters supplied by the user automatically determine which method is used. One may manually call each routine using `rpg.METHOD`. Functions ending in ".R" are pure R implementations.

You may call rpg when n and z are vectors.

## Value

This function returns `num` Polya-Gamma samples.

## References

Nicholas G. Polson, James G. Scott, and Jesse Windle. Bayesian inference for logistic models using Polya-Gamma latent variables. http://arxiv.org/abs/1205.0310

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```h = c(1, 2, 3); z = c(4, 5, 6); ## Devroye-like method -- only use if h contains integers, preferably small integers. X = rpg.devroye(100, h, z); h = c(1.2, 2.3, 3.2); z = c(4, 5, 6); ## Sum of gammas method -- this is slow. X = rpg.gamma(100, h, z); h = c(1, 4, 2.3); z = c(4, 5, 6); ## Hybrid method -- automatically chooses best procedure. X = rpg(100, h, z); ```

BayesLogit documentation built on Sept. 26, 2019, 9:02 a.m.