GT.em {GroupTest}

EM Algorithm

Description

This function estimates all the parameters using the EM algorithm. The iteration is termined when the sum of squared difference of the current updated values and the previous values of the parameters is less than DELTA. A list consisting of all the estimated values of the parameters is returned.

Usage

GT.em(TestStatistic, pi1.ini, pi2.1.ini, L, muL.ini, sigmaL.ini, cL.ini,
DELTA, sigma.KNOWN)

Arguments

TestStatistic

An array of list. Each list of the array corresponds to one group, containing the test statistic, stored as X, and the group size, stored as mg.

L

The number of Gaussian component under the alternative hypothesis.

pi1.ini

Initial value: the probability that a group is significant.

pi2.1.ini

Initial value: the probability that an individual null hypothesis is false given that the group is significant.

muL.ini

Initial value: a vector of means for all the components of the Gaussian mixture.

sigmaL.ini

Initial value: a vector of standard deviation of all the components of the Gaussian mixture.

cL.ini

Initial value: a vector of the probability for all the components of the Gaussian mixture.

DELTA

The criteria to stop the EM algorithm.

sigma.KNOWN

The boolean variable, indicating whether the variance is known.

Value

This function return a list, consisting of the estimated values of all the parameters. The variables within this list are shown as following:

pi1

estimated value of \pi_1, the proportion of a group being significant

pi2.1

estimated value of \pi_{2|1}, the proportion of a null hypothesis being false within a significant group.

muL

a vector of estimated means for all the components of the Gaussian mixture

sigmaL

a vector of estimated standard deviation of all the components of the Gaussian mixture

cL

a vector of the probability for all the components of the Gaussian mixture

L

the number of components in the Gaussian mixture

Examples

data(GroupTest_simulate)
em.estimate <- GT.em( GroupTest_simulate, L=2, pi1.ini=0.7, pi2.1.ini=0.4,
muL.ini=c(-1,1), sigmaL.ini=c(1,2), cL.ini=c(0.4,0.6), DELTA=0.001,
sigma.KNOWN=FALSE )