vash: Main Variance Adaptive SHrinkage function
In mengyin/vashr: Variance Adaptive Shrinkage

Description Usage Arguments Details Value References Examples

Takes vectors of standard errors (sehat), and applies shrinkage to them, using Empirical Bayes methods, to compute shrunk estimates for variances.

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vash(sehat, df, betahat = NULL, randomstart = FALSE, singlecomp = FALSE,
  unimodal = c("auto", "variance", "precision"), prior = NULL, g = NULL,
  estpriormode = TRUE, priormode = NULL, scale = 1, maxiter = 5000)

`sehat`	a p vector of observed standard errors
`df`	scalar, appropriate degree of freedom for (chi-square) distribution of sehat
`betahat`	a p vector of estimates (optional)
`randomstart`	logical, indicating whether to initialize EM randomly. If FALSE, then initializes to prior mean (for EM algorithm) or prior (for VBEM)
`singlecomp`	logical, indicating whether to use a single inverse-gamma distribution as the prior distribution for the variances
`unimodal`	put unimodal constraint on the prior distribution of variances ("variance") or precisions ("precision"). This also can be automatically chosen ("auto") by comparing the likelihoods.
`prior`	string, or numeric vector indicating Dirichlet prior on mixture proportions (defaults to "uniform", or 1,1...,1; also can be "nullbiased" 1,1/k-1,...,1/k-1 to put more weight on first component)
`g`	the prior distribution for variances (usually estimated from the data; this is used primarily in simulated data to do computations with the "true" g)
`estpriormode`	logical, indicating whether to estimate the mode of the unimodal prior
`priormode`	specified prior mode (only works when estpriormode=FALSE).
`scale`	a scalar or a p vector, such that sehat/scale are exchangeable, i.e, can be modeled by a common unimodal prior.
`maxiter`	maximum number of iterations of the EM algorithm

See vignette for more details.

vash returns an object of class "vash", a list with the following elements

`fitted.g`	Fitted mixture prior
`sd.post`	A vector consisting the posterior estimate of standard deviations (square root of variances) from the mixture
`PosteriorPi`	A p*k matrix consisting the mixture proportions of the posterior distribution of variance (k is number of mixture components)
`PosteriorShape`	A p*k matrix consisting the shape parameters of the inverse-gamma posterior distribution of variance (k is number of mixture components)
`PosteriorRate`	A p*k matrix consisting the rate parameters of the inverse-gamma posterior distribution of variance (k is number of mixture components)
`pvalue`	A vector of p-values
`qvalue`	A vector of q-values
`fit`	The fitted mixture object
`unimodal`	Denoting whether unimodal variance prior or unimodal precision prior has been used
`opt.unimodal`	Denoting whether unimodal variance prior or unimodal precision prior model gets higher likelihood
`call`	A call in which all of the specified arguments are specified by their full names
`data`	A list consisting the input sehat, df and betahat

Lu, M., & Stephens, M. (2016). Variance Adaptive Shrinkage (vash): Flexible Empirical Bayes estimation of variances. bioRxiv, 048660.

##An simple example
#generate true variances (sd^2) from an inverse-gamma prior
sd = sqrt(1/rgamma(100,5,5)) 
#observed standard errors are estimates of true sd's
sehat = sqrt(sd^2*rchisq(100,7)/7) 
#run the vash function
fit = vash(sehat,df=7) 
#plot the shrunk sd estimates against the observed standard errors
plot(sehat, fit$sd.post, xlim=c(0,10), ylim=c(0,10)) 

##Running vash with a pre-specified g, rather than estimating it
sd = sqrt(c(1/rgamma(100,5,4),1/rgamma(100,10,9)))
sehat = sqrt(sd^2*rchisq(100,7)/7)
true_g = igmix(c(0.5,0.5),c(5,10),c(4,9)) # define true g 
#Passing this g into vash causes it to i) take the shape and the rate for each component from this g, 
#and ii) initialize pi to the value from this g.
se.vash = vash(sehat, df=7, g=true_g)