R: Performs adaptive shrinkage on Poisson data

ash_pois {ashr} | R Documentation

## Performs adaptive shrinkage on Poisson data

### Description

Uses Empirical Bayes to fit the model

y_j | λ_j ~ Poi(c_j λ_j)

with

h(lambda_j) ~ g()

where h is a specified link function (either "identity" or "log" are permitted).

### Usage

    ash_pois(y, scale = 1, link = c("identity", "log"), ...)

### Arguments

`y` | vector of Poisson observations.
`scale` | vector of scale factors for Poisson observations: the model is y[j]~Pois(scale[j]*lambda[j]).
`link` | string, either "identity" or "log", indicating the link function.
`...` | other parameters to be passed to ash

### Details

The model is fit in two stages: i) estimate g by maximum likelihood (over the set of symmetric unimodal distributions) to give estimate \hat{g}; ii) Compute posterior distributions for λ_j given y_j,\hat{g}. Note that the link function h affects the prior assumptions (because, e.g., assuming a unimodal prior on λ is different from assuming unimodal on \logλ), but posterior quantities are always computed for the for λ and *not* h(λ).

### Examples

       beta = c(rep(0,50),rexp(50))
       y = rpois(100,beta) # simulate Poisson observations
       y.ash = ash_pois(y,scale=1)

[Package ashr version 2.2-54 Index]