gaussianSamples: Simulate equi-correlated data

In pneuvial/sanssouci: Post Hoc Multiple Testing Inference

Simulate equi-correlated data

Description

Simulate equi-correlated data coming from one or two populations

Usage

gaussianSamples(m, rho, n, pi0, SNR = 1, prob = 1, w = NULL)

Arguments

m	Number of hypotheses
rho	Level of equi-correlation between pairs of variables
n	Number of observations, i.e. sample size
pi0	Proportion of true null hypotheses
SNR	Signal to noise ratio. Either a numeric value (a measure of distance between H0 and H1) or a vector of length m*(1-pi0)
prob	A numeric value in (0, 1], the frequency of the population under H1. If prob=1 (the default), a data set from a single population is generated.
w	An optional vector of length n, the underlying factor driving equi-correlation

Details

If prob = 1, each of m_1 variables under H_1 has mean SNR/\sqrt(n). If 0 < p < 1, then n_0 samples are drawn from a \mathcal{N}(0,1) distribution while n_1 are drawn from a \mathcal{N}(\mu, 1) distribution, where \mu = SNR*\sqrt(1/(n_0) + 1/n_1). The argument p is the probability of a sample to belong to the non-zero-mean population.

Value

A list with three elements:

X

An m x n matrix of m-dimensional Gaussian observations, where m1 rows are under H1, and m0 rows are under H0, with m0/m = pi0

categ

A numeric vector of length n matching each observation to a sample (in 0 or 1)

H

A vector of length m, the status of each hypothesis: 0 for true null hypothesis, and 1 for true alternative hypothesis

.

Author(s)

Gilles Blanchard, Pierre Neuvial and Etienne Roquain

See Also

SansSouciSim

Examples

m <- 23
rho <- 0.2
n <- 100
pi0 <- 0.5
B <- 1e3

## two-sample data
sim <- gaussianSamples(m, rho, n, pi0, SNR = 2, prob = 0.5)
tests <- testByRandomization(sim$X, sim$categ, B = B)

## show test statistics
pch <- 20
colStat <- 1+sim$H
plot(tests$T, col=colStat, main="Test statistics", pch=pch)
legend("topleft", c("H0", "H1"), pch=pch, col=1:2)

## one-sample data
sim <- gaussianSamples(m, rho, n, pi0, SNR=2)
tests <- testByRandomization(sim$X, B = B)

## show test statistics
pch <- 20
colStat <- 1+sim$H
plot(tests$T, col=colStat, main="Test statistics", pch=pch)
legend("topleft", c("H0", "H1"), pch=pch, col=1:2)

pneuvial/sanssouci documentation built on Feb. 12, 2024, 4:18 a.m.