The Fiducialist Papers: Evidence and Likelihood

D. R. Bickel, “Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions,” Technical Report, Ottawa Institute of Systems Biology, arXiv:1106.4490 (2011). Full preprint

To address multiple comparison problems in small-to-high-dimensional biology, this paper introduces novel estimators of the local false discovery rate (LFDR), reports their main properties, and illustrates their use with proteomics data. Unlike previous LFDR estimators, the new estimators have all of the following advantages:

1. proven asymptotic conservatism;
2. simplicity of calculation without the tuning of smoothing parameters;
3. no strong parametric assumptions;
4. applicability to very small numbers of hypotheses as well as to very large numbers of hypotheses.