tfromw {EbayesThresh}

Find threshold from mixing weight

Description

Given a single value or a vector of weights (i.e. prior probabilities that the parameter is nonzero) and sampling standard deviations (sd equals 1 for Cauchy prior), find the corresponding threshold(s) under the specified prior.

Usage

  tfromw(w, s = 1, prior = "laplace", bayesfac = FALSE, a = 0.5)

  laplace.threshzero(x, s = 1, w = 0.5, a = 0.5)

  cauchy.threshzero(z, w)

Arguments

x

Parameter value passed to laplace.threshzero objective function.

w

Prior weight or vector of weights.

s

A single value or a vector of standard deviations if the Laplace prior is used. If w is a vector, must have the same length as w. Ignored if Cauchy prior is used.

prior

Specification of prior to be used; can be "cauchy" or "laplace".

bayesfac

Specifies whether Bayes factor threshold should be used instead of posterior median threshold.

a

Scale factor if Laplace prior is used. Ignored if Cauchy prior is used.

z

The putative threshold vector for cauchy.threshzero.

Details

The Bayes factor method uses a threshold such that the posterior probability of zero is exactly half if the data value is equal to the threshold. If bayesfac is set to FALSE (the default) then the threshold is that of the posterior median function given the data value.

The routine carries out a binary search over each component of an appropriate vector function, using the routine vecbinsolv.

For the posterior median threshold, the function to be zeroed is laplace.threshzero or cauchy.threshzero.

For the Bayes factor threshold, the corresponding functions are beta.laplace or beta.cauchy.

Value

The value or vector of values of the estimated threshold(s).

Author(s)

Bernard Silverman

References

See ebayesthresh and http://www.bernardsilverman.com

See Also

wfromx, tfromx, wandafromx

Examples

tfromw(c(0.05, 0.1), s = 1) 
tfromw(c(0.05, 0.1), prior = "cauchy", bayesfac = TRUE)