gen_exp_family: Generate exp_family Objects for Exponential Families

In adaptMT: Adaptive P-Value Thresholding for Multiple Hypothesis Testing with Side Information

Description

exp_family objects contain all required information in an exponential family to perform the E-step. The exponential function is encoded by

h(p; η) = exp{(η(μ) - η(μ*)) g(p) - (A(μ) - A(μ*))}

where g(p) is an arbitrary transformation, μ is the mean parameter, η is the natural parameter, and A(μ) is the partition function. The extra redundant parameter μ* is to guarantee that U([0, 1]) belongs to the class.

Usage

gen_exp_family(g, ginv, eta, mustar, A, name = NULL, family = NULL)

beta_family()

inv_gaussian_family()

Arguments

g	a function. An transformation of p-values
ginv	a function. The inverse function of g
eta	a function. The natural parameter as a function of the mean parameter mu
mustar	a scalar. The mean parameter that gives U([0, 1])
A	a function. The partition function
name	a string. A name for the family. NULL by default
family	an object of class "family" from stats package. The family used for model fitting in glm, gam, glmnet, etc..

Details

Beta family (beta_family()): modeling p-values as Beta-distributed random variables, i.e. g(p) = -log(p), η(μ) = -1 / μ, μ* = 1, A(μ) = log(μ), name = "beta" and family = Gamma(). Beta-family is highly recommended for general problems and used as default.

Inverse-gaussian family (inv_gaussian_family()): modeling p-values as transformed z-scores, i.e. g(p) = Φ^{-1}(p) (Φ is the c.d.f. of a standard normal random variable), η(μ) = μ, μ* = 0, A(μ) = μ^2 / 2, name = "inv_gaussian" and family = gaussian().

Value

an object of class "exp_family". This includes all inputs and h, the density function.

adaptMT documentation built on May 1, 2019, 10:15 p.m.