ebnm_deconvolver: Solve the EBNM problem using the "deconvolveR" family of distributions

Description

Solves the empirical Bayes normal means (EBNM) problem using a non-parametric exponential family with a natural spline basis. Like ebnm_npmle, there is no unimodal assumption, but whereas ebnm_npmle produces spiky estimates for $g$, ebnm_deconvolver estimates are much more regular. See deconvolveR-package for details and references. Identical to function ebnm with argument prior_family = "deconvolver".

Usage

ebnm_deconvolver(
  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 sampler takes a single parameter nsamp, the number of posterior samples to return per observation.

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: Standard errors, which must be uniformly equal to 1 (i.e., s = 1) since the deconvolveR method takes $z$-scores as input.
scale: A deconvolveR prior is a finite mixture of point masses $$\pi_1 \delta_{\mu_1} + \ldots + \pi_K \delta_{\mu_K},$$ where parameters $\pi_k$ are estimated and the point masses are evenly spaced over $(\mu_1, \mu_K)$.The distance between successive point masses can be specified by the user via parameter scale, in which case the argument should be a scalar specifying the distance $d = \mu_2 - \mu_1 = \cdots = \mu_K - \mu_{K - 1}$; alternatively, if scale = "estimate", then ebnm sets the grid via function ebnm_scale_npmle.
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. This has the side effect of fixing the scale parameter. When supplied, g_init should be an object of class normalmix or an ebnm object in which the fitted prior is an object of class normalmix.
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 optimization function nlm.
...: Additional parameters to be passed to function deconv in package deconvolveR.