ebnm_unimodal_nonpositive: Solve the EBNM problem using unimodal nonpositive distributions

Description

Solves the empirical Bayes normal means (EBNM) problem using the family of unimodal distributions with support constrained to be less than the mode. Identical to function ebnm with argument prior_family = "unimodal_nonpositive". For details about the model, see ebnm.

Usage

ebnm_unimodal_nonpositive(
  x,
  s = 1,
  mode = 0,
  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: 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 $g$ or "estimate" if the mode is to be estimated from the data.
scale: The nonparametric family of nonnpositive unimodal distributions is approximated via a finite mixture of uniform distributions $$\pi_1 \mathrm{Unif}(\mu - a_1, \mu) + \ldots + \pi_K \mathrm{Unif}(\mu - a_K, \mu),$$ where parameters $\pi_k$ are estimated and the grid of lengths $(a_1, \ldots, a_K)$ is fixed in advance. By making the grid sufficiently dense, one can obtain an arbitrarily good approximation. The grid can be specified by the user via parameter scale, in which case the argument should be the vector of lengths $(a_1, \ldots, a_K)$; alternatively, if scale = "estimate", then ebnm sets the grid via function ebnm_scale_unimix. Note that ebnm sets the grid differently from function ash. To use the ash grid, set scale = "estimate" and pass in gridmult as an additional parameter. See ash for defaults and details.
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 mode and scale parameters. When supplied, g_init should be an object of class unimix or an ebnm object in which the fitted prior is an object of class unimix.
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 mixsqp.
...: Additional parameters to be passed to function ash in package ashr.