ashr (version 2.2-63)

ash_pois: Performs adaptive shrinkage on Poisson data

Description

Uses Empirical Bayes to fit the model $$y_j|{\lambda }_{j}Poi(c_j{\lambda }_j)$$ with $$h(lambd{a}_j)g()$$ 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 $y[j]Pois(scale[j]\ast lambda[j])$.

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 ${\lambda }_j$ given $y_j,\hat{g}$. Note that the link function $h$ affects the prior assumptions (because, e.g., assuming a unimodal prior on $\lambda$ is different from assuming unimodal on $\log \lambda$), but posterior quantities are always computed for the for $\lambda$ and *not* $h(\lambda )$.

Examples

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