Estimate the mixture gamma-normal (MGN) distribution using expectation-maximization (EM) algorithm

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Description

the MGN distribution model the joint distribution, pi(lambda,delta), by a K-component MGN distribution, and allows degenerate normal for delta when the null hypothesis is simple.

Usage

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MGN.EM(data, nK, p0 = NULL, d0 = 0, nK0 = 0, iter.max = 10, print.steps = FALSE, MGN0 = NULL, model = NULL, nMC = 10000)

Arguments

data

the RNA-seq data, should be the output from RNASeq.Data

nK

the number of components in MGN. When testing for fold-changes (FC), nK includes all components, when testing for differential expression (DE), nK only includes the components that are NOT degenerated.

p0

the proportion of null genes when testing for DE genes.

d0

the point where 'delta' is degerated, default is 0 when testing for DE genes.

nK0

the number of components that are degenerated when testing for DE genes.

iter.max

maximium number of interations in the EM algorithm

print.steps

print the esimates of MGN in each iteration step, if TRUE. Default is FALSE

MGN0

The initialization of the MGN. It should be a data.frame with 5 columns: pr, alpha, beta, mu, sigma. The methods of moment estimation will be used if not provided.

model

data model, can be 'nbinom' or 'poisson'. the default will be the same as in 'data'

nMC

the number of random samples from Gamma and Normal distrubitons in the Monte-Carlo simulation.

Value

MGN

The estimated MGN distribution, as a data.frame with 5 columns: pr, alpha,beta,mu,sigma. pr: the proportion (weight) of each component \ alpha: alpha in the Gamma distribution \ beta: beta in the Gamma distribution \ mu: mu (mean) of the Normal distribution\ sigma: sigma (standard deviation) of the Normal distribution. sigma=0 is allowed for degenerated Normal

lam

the shrinked estimation of lambda (mean expression for each gene)

del

the shrinked estimation of delta (log-fold change) for each gene

Examples

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#### see examples by typing 'help(test.AMAP)'