Description Usage Arguments Details Value Author(s) References See Also
View source: R/utils_sdPrior.r
Compute Density Function of Approximated (Differentiably) Uniform Distribution.
1 | dapprox_unif(x, scale, tildec = 13.86294)
|
x |
denotes the argument of the density function. |
scale |
the scale parameter originally defining the upper bound of the uniform distribution. |
tildec |
denotes the ratio between scale parameter θ and s. The latter is responsible for the closeness of the approximation to the uniform distribution. See also below for further details and the default value. |
The density of the uniform distribution for τ is approximated by
p(τ)=(1/(1+exp(τ\tilde{c}/θ-\tilde{c})))/(θ(1+log(1+exp(-\tilde{c}))))
. This results in
p(τ^2)=0.5*(τ^2)^(-1/2)(1/(1+exp((τ^2)^(1/2)\tilde{c}/θ-\tilde{c})))/(θ(1+log(1+exp(-\tilde{c}))))
for tau^2. \tilde{c} is chosen such that P(τ<=θ)>=0.95.
the density.
Nadja Klein
Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.
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