R: Solve the EBNM problem using symmetric unimodal distributions

ebnm_unimodal_symmetric {ebnm}

R Documentation

Solve the EBNM problem using symmetric unimodal distributions

Description

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

Usage

ebnm_unimodal_symmetric(
  x,
  s = 1,
  mode = 0,
  scale = "estimate",
  g_init = NULL,
  fix_g = FALSE,
  output = ebnm_output_default(),
  control = NULL,
  ...
)

Arguments

`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` or `"estimate"` if the mode is to be estimated from the data.
`scale`	The nonparametric family of symmetric unimodal distributions is approximated via a finite mixture of uniform distributions `\pi_1 \mathrm{Unif}(\mu - a_1, \mu + a_1) + \ldots + \pi_K \mathrm{Unif}(\mu - a_K, \mu + a_K),` where parameters `\pi_k` are estimated and the grid of (half-)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 `(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`.

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.