Moment and inverse moment prior elicitation.

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Description

mode2g finds the g value corresponding to a given prior mode. g2mode finds the prior mode corresponding to a given g value. priorp2g finds the g value giving priorp prior probability to the interval (-q,q).
All routines operate in the standardized effect sizes scale.

Usage

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mode2g(prior.mode, prior=c("iMom", "normalMom", "tMom"), nu=1, dim=1)
g2mode(g, prior=c("iMom", "normalMom", "tMom"), nu=1, dim=1)
priorp2g(priorp, q, nu=1, prior=c("iMom", "normalMom", "tMom"))

Arguments

prior.mode

Prior mode for the quadratic form (theta-theta0)' * solve(Sigma) * (theta-theta0)/(n*g*sigma^2), where sigma is the dispersion parameter and Sigma is given by the design matrix.

prior

prior=='normalMom' does computations for the normal moment prior, prior=='tMom' for the T moment prior, prior=='iMom' does computations for the inverse moment prior. Currently prior=='tMom' is not implemented in priorp2g.

nu

Prior degrees of freedom for the T moment prior or the iMom prior (ignored if prior=='normalMom').

dim

Dimensionality of the parameter, i.e. dim==1 for univariate, dim==2 for bivariate and so on.

g

Prior parameter. See dimom for details.

priorp

priorp2g returns g giving priorp prior probability to the interval (-q,q).

q

priorp2g returns g giving priorp prior probability to the interval (-q,q).

Details

See dmom and dimom for details on the meaning of the prior parameters.

Value

mode2g returns the value of the prior parameter g matching the given mode.

g2mode returns the prior mode for a given prior parameter g.

priorp2g returns g giving priorp prior probability to the interval (-q,q).

Author(s)

David Rossell rosselldavid@gmail.com

References

See http://rosselldavid.googlepages.com for technical reports.

See Also

dmom, dimom, mombf, imombf

Examples

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#find g value giving a prior mode for (theta/(sigma*n*Sigma))^2 at 0.2^2
data(hald)
lm1 <- lm(hald[, 1] ~ hald[, 2] + hald[, 3] + hald[, 4] + hald[, 5])
prior.mode <- .2
gmom <- mode2g(prior.mode^2, prior='normalMom')
gtmom <- mode2g(prior.mode^2, prior='tMom', nu=3)
gimom <- mode2g(prior.mode^2, prior='iMom')
gmom
gimom

#find g value giving 0.05 probability to interval (-.2,.2)
priorp <- .05; q <- .2
gmom <- priorp2g(priorp=priorp, q=q, prior='normalMom')
gimom <- priorp2g(priorp=priorp, q=q, prior='iMom')
gmom
gimom