R: Find threshold from mixing weight

tfromw {EbayesThresh} | R Documentation

## 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)

[Package EbayesThresh version 1.4-12 Index]