R: E-step for parameterized bivariate 2-component Gaussian...

e.step.2normal {idr} | R Documentation

## 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)

[Package idr version 1.2 Index]