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