kappa_moments: Moments for shrinkage and number of effective parameters
In jrnold/bayz: Miscellaneous Bayesian functions

Description Usage Arguments Details Value

Means and variances for the shrinkage parameter, kappa, and the number of effective parameters, m_{eff}, in regression problems using scale-mixture of normal shrinkage priors.

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kappa_moments(tau, sigma = 1, n = 1)

meff_moments(tau, sigma = 1, n = 1, D = 1)

`tau`	Numeric. The global scale parameter.
`sigma`	Numeric. The observation disturbance scale parameter.
`n`	Integer. The number of observations.
`D`	Integer. The number of parameters.

The mean and variance for the shrinkage parameter κ given the global scale τ, and observation disturbance scale σ are: \begin{aligned}[t]\ E(κ_j | τ, σ) &= \frac{1}{1 + σ^{-1} τ √{n}} , \\ Var(κ_j | τ, σ) &= \frac{σ^{-1} τ √{n}}{2(1 + σ^{-1} τ √{n})^2} \\ \end{aligned} Likewise, the mean and variance for the number of effective parameters m_{eff} for D parameters is, \begin{aligned}[t] E(m_{eff} | τ, σ) &= \frac{1}{1 + σ^{-1} τ √{n}} D, \\ Var(m_{eff} | τ, σ) &= \frac{σ^{-1} τ √{n}}{2(1 + σ^{-1} τ √{n})^2} D . \\ \end{aligned}

kappa_moments: A data frame with columns: tau, sigma, n, mean, and var.
meff_moments: A data frame with columns: tau, sigma, n, D, mean, and var.