ebpm_gamma: Empirical Bayes Poisson Mean with Gamma Prior

In stephenslab/ebpm: What the Package Does (One Line, Title Case)

Empirical Bayes Poisson Mean with Gamma Prior

Description

Uses Empirical Bayes to fit the model

x_j | \lambda_j ~ Poi(s_j \lambda_j)

with

lambda_j ~ g()

with Point Gamma: g() = gamma(shape, scale)

Usage

ebpm_gamma(x, s = 1, g_init = NULL, fix_g = F, control = NULL)

Arguments

x	vector of Poisson observations.
s	vector of scale factors for Poisson observations: the model is y[j]~Pois(scale[j]*lambda[j]).
g_init	The prior distribution g, of the class point_gamma, with pi0 set to 0. Usually this is left unspecified (NULL) and estimated from the data. However, it can be used in conjuction with fix_g = TRUE to fix the prior (useful, for example, to do computations with the "true" g in simulations). If g_init is specified but fix_g = FALSE, g_init specifies the initial value of g used during optimization.
fix_g	If TRUE, fix the prior g at g_init instead of estimating it.
control	A list of control parameters to be passed to the optimization function. 'nlm' is used.

Details

The model is fit in two stages: i) estimate g by maximum likelihood (over shape, scale) (it's in fact Negative Binomial) ii) Compute posterior distributions for \lambda_j given x_j,\hat{g}.

Value

A list containing elements:

posterior

A data frame of summary results (posterior means, and posterior log mean).

fitted_g

The fitted prior \hat{g} of class point_gamma, with pi0 equal 0

log_likelihood

The optimal log likelihood attained L(\hat{g}).

Examples

   beta = c(rep(0,50),rexp(50))
   x = rpois(100,beta) # simulate Poisson observations
   s = replicate(100,1)
   out = ebpm_gamma(x,s)

stephenslab/ebpm documentation built on Oct. 19, 2023, 1 p.m.