ebnm_scale_normalmix: Set scale parameter for scale mixtures of normals
In ebnm: Solve the Empirical Bayes Normal Means Problem

ebnm_scale_normalmix

R Documentation

Set scale parameter for scale mixtures of normals

The default method for setting the scale parameter for function ebnm_normal_scale_mixture.

ebnm_scale_normalmix(
  x,
  s,
  mode = 0,
  min_K = 3,
  max_K = 300,
  KLdiv_target = 1/length(x)
)

`x`	A vector of observations. Missing observations (`NA`s) are not allowed.
`s`	A vector of standard errors (or a scalar if all are equal). Standard errors may not be exactly zero, and missing standard errors are not allowed.
`mode`	A scalar specifying the mode of the prior `g`.
`min_K`	The minimum number of components `K` to include in the finite mixture of normal distributions used to approximate the nonparametric family of scale mixtures of normals.
`max_K`	The maximum number of components `K` to include in the approximating mixture of normal distributions.
`KLdiv_target`	The desired bound `\kappa` on the KL-divergence from the solution obtained using the approximating mixture to the exact solution. More precisely, the scale parameter is set such that given the exact MLE `\hat{g} := \mathrm{argmax}_{g \in G} L(g),` where `G` is the full nonparametric family, and given the MLE for the approximating family `\tilde{G}` `\tilde{g} := \mathrm{argmax}_{g \in \tilde{G}} L(g),` we have that `\mathrm{KL}(\hat{g} \ast N(0, s^2) \mid \tilde{g} \ast N(0, s^2)) \le \kappa,` where `\ast \ N(0, s^2)` denotes convolution with the normal error distribution (the derivation of the bound assumes homoskedastic observations). For details, see References below.