polynomial_transformation: constructs a polynomial transformation for use with functions...

In PoissonPCA: Poisson-Noise Corrected PCA

Description

When we are dealing with a transformation of the latent Poisson mean Lambda, we need various useful functions. This function computes the necessary functions for a polynomial, and returns a list of the required functions.

Usage

polynomial_transformation(coeffs)

Arguments

coeffs

A vector of coefficents of the polynomial. The constant term should not be included.

Details

The coefficients of the polynomial should be given in order of decreasing degree, and should not include the constant term. For example "coeffs"=c(1,2,3) refers to the polynomial X^3+2*X^2+3*X. This function returns a list of functions for dealing with this transformation.

Value

f	evaluates the transformation
g	an estimator for the transformation of a latent Poisson mean
solve	computes the inverse transformation (often used for simulations)
CVar	an estimator for the conditional variance of g(X)

Author(s)

Toby Kenney [e-mail] and Tianshu Huang

Examples

cubic<-polynomial_transformation(c(1,0,0))

X<-rpois(100,1.8^3)

gX<-X
varX<-X
for(i in 1:100){
gX[i]<-cubic$g(X[i])
varX[i]<-cubic$CVar(X)
}
mean(gX)
var(gX)
mean(varX)

PoissonPCA documentation built on Aug. 17, 2021, 5:09 p.m.