Fit a mixture of beta distributions in p-values {MXM}

Fit a mixture of beta distributions in p-values

Description

Fit a mixture of beta distributions in p-values.

Usage

pval.mixbeta(p)

Arguments

p

A vector of p-values.

Details

The p-values are assumed to follow a mixture of two beta distributions. The null p-values follow Be(1, 1) and the non-null p-values follow Be(\xi, 1). In the first step, the proportion of true null values using Storey and Tibshirani (2003) is calculated and then MLE is adopted to obtain \xi. For more information on this see Triantafillou (2014).

Value

A vector with the estimated \pi_0 and \xi values.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris [e-mail]

References

Triantafillou S., Tsamardinos I. and Roumpelaki A. (2014). Learning neighborhoods of high confidence in constraint-based causal discovery. In European Workshop on Probabilistic Graphical Models, pp. 487-502.

Storey J.D. and Tibshirani R. (2003). Statistical significance for genome-wide experiments. Proceedings of the National Academy of Sciences, 100: 9440-9445.

See Also

pc.skel, mmhc.skel, corfs.network, local.mmhc.skel, conf.edge.lower

Examples

## simulate a dataset with continuous data
y <- rdag2(400, p = 25, nei = 3)
ind <- sample(1:25, 25)
x <- y$x[, ind]
mod <- pc.skel( x, method = "comb.fast", alpha = 0.01 ) 
pval <- as.vector( mod$pvalue[lower.tri(mod$pvalue)] )
pval.mixbeta(pval)