ebnm_scale_unimix: Set scale parameter for nonparametric unimodal prior families

In ebnm: Solve the Empirical Bayes Normal Means Problem

Set scale parameter for nonparametric unimodal prior families

Description

The default method for setting the scale parameter for functions ebnm_unimodal, ebnm_unimodal_symmetric, ebnm_unimodal_nonnegative, and ebnm_unimodal_nonpositive.

Usage

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

Arguments

x	A vector of observations. Missing observations (NAs) 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 uniform distributions used to approximate the nonparametric family of unimodal distributions.
max_K	The maximum number of components K to include in the approximating mixture of uniform 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.

References

Jason Willwerscheid (2021). Empirical Bayes Matrix Factorization: Methods and Applications. University of Chicago, PhD dissertation.

ebnm documentation built on Oct. 13, 2023, 1:16 a.m.