Bayesian false discovery rate selection

Selects the largest set of hypotheses whose posterior expected false discovery rate is at most alpha, using the direct posterior probability approach (Newton et al. 2004). Hypotheses are ranked by their posterior probability prob; the expected FDR of the top \(k\) is the mean of \(1 - prob\) over them.

Usage

bayes_fdr(prob, alpha = 0.05)

Arguments

prob

Numeric vector of posterior probabilities, or a symmetric matrix of edge probabilities (only the upper triangle is used).

alpha

Target posterior expected FDR. Default 0.05.

Value

A logical vector, or a symmetric logical matrix with FALSE diagonal, marking the selected hypotheses. Attributes: expected_fdr (posterior expected FDR of the selected set), n_selected, cutoff (smallest selected probability, or NA) and alpha.

Details

The guarantee is only as good as the calibration of prob. For differential edges, pass a probability of a real difference such as \(P(|D| > c)\) or \(P(g_k \ne g_m)\), not a sign probability (see diff_summary()). Ties at the cutoff are broken by input order.

References

Newton, M.A., Noueiry, A., Sarkar, D. & Ahlquist, P. (2004). Detecting differential gene expression with a semiparametric hierarchical mixture method. Biostatistics, 5(2), 155-176.

See also

select_diff_edges()

Examples

bayes_fdr(c(0.99, 0.97, 0.9, 0.6, 0.2), alpha = 0.05)
#> [1]  TRUE  TRUE  TRUE FALSE FALSE
#> attr(,"expected_fdr")
#> [1] 0.04666667
#> attr(,"n_selected")
#> [1] 3
#> attr(,"cutoff")
#> [1] 0.9
#> attr(,"alpha")
#> [1] 0.05