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 $$h(lambda_j) ~ g()$$ 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 \(\lambda_j\) 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)