Performs adaptive shrinkage on Poisson data
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).
ash_pois(y, scale = 1, link = c("identity", "log"), ...)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 |
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).
beta = c(rep(0,50),rexp(50)) y = rpois(100,beta) # simulate Poisson observations y.ash = ash_pois(y,scale=1)
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