Moment prior and inverse moment prior.
Description
dmom
, dimom
and demom
return the density for the
moment, inverse moment and exponential moment priors.
pmom
, pimom
and pemom
return the distribution function for the univariate
moment, inverse moment and exponential moment priors (respectively).
qmom
and qimom
return the quantiles for the univariate
moment and inverse moment priors.
Usage
1 2 3 4 5 6 7 8 9 10 11  dmom(x, tau, a.tau, b.tau, phi=1, r=1, V1, baseDensity='normal', nu=3,
logscale=FALSE, penalty='product')
dimom(x, tau=1, phi=1, V1, logscale=FALSE, penalty='product')
demom(x, tau, a.tau, b.tau, phi=1, logscale=FALSE)
pmom(q, V1 = 1, tau = 1)
pimom(q, V1 = 1, tau = 1, nu = 1)
pemom(q, tau, a.tau, b.tau)
qmom(p, V1 = 1, tau = 1)
qimom(p, V1 = 1, tau = 1, nu = 1)

Arguments
x 
In the univariate setting, 
q 
Vector of quantiles. 
p 
Vector of probabilities. 
V1 
Scale matrix (ignored if 
tau 
Prior dispersion parameter is 
a.tau 
If 
b.tau 
See 
phi 
Prior dispersion parameter is 
r 
Prior power parameter for MOM prior is 
baseDensity 
For 
nu 
Prior parameter indicating the degrees of freedom for the
quadratic T MOM and iMOM prior densities. The
tails of the inverse moment prior are proportional to the tails of a
multivariate T with 
penalty 

logscale 
For 
Details
For type=='quadratic'
the density is as follows.
Define the quadratic form q(theta)= (thetatheta0)' *
solve(V1) * (thetatheta0) / (tau*phi).
The normal moment prior density is proportional to
q(theta)*dmvnorm(theta,theta0,tau*phi*V1).
The T moment prior is proportional to
q(theta)*dmvt(theta,theta0,tau*phi*V1,df=nu).
The inverse moment prior density is proportional to
q(theta)^((nu+d)/2) * exp(1/q(theta))
.
pmom, pimom and qimom use closedform expressions, while qmom uses nlminb to find quantiles numerically. Only the univariate version is implemented. In this case the product MOM is equivalent to the quadratic MOM. The same happens for the iMOM.
Only the product eMOM prior is implemented.
Value
dmom
returns the value of the moment prior density.
dimom
returns the value of the inverse moment prior density.
Author(s)
David Rossell
References
Johnson V.E., Rossell D. NonLocal Prior Densities for Default Bayesian Hypothesis Tests. Journal of the Royal Statistical Society B, 2010, 72, 143170.
Johnson V.E., Rossell D. Bayesian model selection in highdimensional settings. Technical report. 2011
See http://rosselldavid.googlepages.com for technical reports.
See Also
g2mode
to find the
prior mode corresponding to a given g
. mode2g
to find the g value corresponding to a given prior mode.
Examples
1 2 3 4 5 6 