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

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

## M-step for parameterized bivariate 2-component Gaussian mixture models

### Description

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

### Usage

    m.step.2normal(z.1, z.2, e.z)

### Arguments

`z.1` | a numerical data vector on coordinate 1.
`z.2` | a numerical data vector on coordinate 2.
`e.z` | a vector of expected conditional probability that the $i$th observation is reproducible.

### Details

This function is used in the EM algorithm for estimating the parameters of the Gaussian mixture model at the latent copula space.

### Value

Estimated parameters, basically a list including elements

`p` | the estimated mixing proportion of the reproducible component.
`mu` | the estimated mean for the reproducible component.
`sigma` | the estimated standard deviation of the reproducible component.
`rho` | the estimated correlation coefficient of 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

`e.step.2normal`, `loglik.2binormal`, `est.IDR`

### Examples

    ##---- Should be DIRECTLY executable !! ----
    ##-- ==>  Define data, use random,
    ##--	or do  help(data=index)  for the standard data sets.

    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)))
    e.z <- c(rep(0, 500) + abs(rnorm(0, 0.05)), rep(1, 500)-abs(rnorm(0, 0.05)))

    para <- m.step.2normal(z.1, z.2, e.z)

    para

[Package idr version 1.2 Index]