ash_pois {ashr}

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)