ebnm_horseshoe: Solve the EBNM problem using horseshoe priors

Description

Solves the empirical Bayes normal means (EBNM) problem using the family of horseshoe distributions. Identical to function ebnm with argument prior_family = "horseshoe". For details about the model, see ebnm.

Usage

ebnm_horseshoe(
  x,
  s = 1,
  scale = "estimate",
  g_init = NULL,
  fix_g = FALSE,
  output = ebnm_output_default(),
  control = NULL
)

Value

An ebnm object. Depending on the argument to output, the object is a list containing elements:

data: A data frame containing the observations x and standard errors s.
posterior: A data frame of summary results (posterior means, standard deviations, second moments, and local false sign rates).
fitted_g: The fitted prior \(\hat{g}\).
log_likelihood: The optimal log likelihood attained, \(L(\hat{g})\).
posterior_sampler: A function that can be used to produce samples from the posterior. The function takes parameters nsamp, the number of posterior samples to return per observation, and burn, the number of burn-in samples to discard (an MCMC sampler is used).

S3 methods coef, confint, fitted, logLik,

nobs, plot, predict, print, quantile,

residuals, simulate, summary, and vcov

have been implemented for ebnm objects. For details, see the respective help pages, linked below under See Also.

Arguments

x: A vector of observations. Missing observations (NAs) are not allowed.
s: A scalar specifying the standard error of the observations (observations must be homoskedastic).
scale: A scalar corresponding to \(s\tau\) in the usual parametrization of the horseshoe distribution, or "estimate" if this parameter is to be estimated from the data.
g_init: The prior distribution \(g\). Usually this is left unspecified (NULL) and estimated from the data. However, it can be used in conjuction with fix_g = TRUE to fix the prior (useful, for example, to do computations with the "true" \(g\) in simulations). If g_init is specified but fix_g = FALSE, g_init specifies the initial value of \(g\) used during optimization. When supplied, g_init should be an object of class horseshoe or an ebnm object in which the fitted prior is an object of class horseshoe.
fix_g: If TRUE, fix the prior \(g\) at g_init instead of estimating it.
output: A character vector indicating which values are to be returned. Function ebnm_output_default() provides the default return values, while ebnm_output_all() lists all possible return values. See Value below.
control: A list of control parameters to be passed to function optimize.