e.step.2normal: E-step for parameterized bivariate 2-component Gaussian...

In idr: Irreproducible Discovery Rate

E-step for parameterized bivariate 2-component Gaussian mixture models

Description

Expectation step in the EM algorithm for parameterized bivariate 2-component Gaussian mixture models with (1-p)N(0, 0, 1, 1, 0) + pN(mu, mu, sigma, sigma, rho).

Usage

e.step.2normal(z.1, z.2, mu, sigma, rho, p)

Arguments

z.1	a numerical data vector on coordinate 1.
z.2	a numerical data vector on coordinate 2.
mu	mean for the reproducible component.
sigma	standard deviation of the reproducible component.
rho	correlation coefficient of the reproducible component.
p	mixing proportion of the reproducible component.

Value

e.z	a numeric vector, where each entry represents the estimated expected conditional probability that an observation is in the reproducible component.

Author(s)

Qunhua Li

References

Q. Li, J. B. Brown, H. Huang and P. J. Bickel. (2011) Measuring reproducibility of high-throughput experiments. Annals of Applied Statistics, Vol. 5, No. 3, 1752-1779.

See Also

m.step.2normal, loglik.2binormal, est.IDR

Examples

z.1 <- c(rnorm(500, 0, 1), rnorm(500, 3, 1))
rho <- 0.8

## The component with higher values is correlated with correlation coefficient=0.8 
z.2 <- c(rnorm(500, 0, 1), rnorm(500, 3 + 0.8*(z.1[501:1000]-3), (1-rho^2)))

## Starting values
mu0 <- 3
sigma0 <- 1
rho0 <- 0.85
p0 <- 0.55

e.z <- e.step.2normal(z.1, z.2, mu0, sigma0, rho0, p0)

idr documentation built on June 21, 2022, 9:05 a.m.