Statistical inference optimized with respect to the observed sample for single or multiple comparisons

@article{Bickel2010StatisticalIO,
  title={Statistical inference optimized with respect to the observed sample for single or multiple comparisons},
  author={David R. Bickel},
  journal={ArXiv},
  year={2010},
  volume={abs/1010.0694}
}
  • D. Bickel
  • Published 4 October 2010
  • Computer Science
  • ArXiv
The normalized maximum likelihood (NML) is a recent penalized likelihood that has properties that justify defining the amount of discrimination information (DI) in the data supporting an alternative hypothesis over a null hypothesis as the logarithm of an NML ratio, namely, the alternative hypothesis NML divided by the null hypothesis NML. The resulting DI, like the Bayes factor but unlike the p-value, measures the strength of evidence for an alternative hypothesis over a null hypothesis such… 

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References

SHOWING 1-10 OF 53 REFERENCES
THE STRENGTH OF STATISTICAL EVIDENCE FOR COMPOSITE HYPOTHESES: INFERENCE TO THE BEST EXPLANATION
TLDR
The proposed method of weighing evidence almost always favors the correct hypothesis under mild regularity conditions, and issues with simultaneous inference and multiplicity are addressed.
A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion
Abstract To compute a Bayes factor for testing H 0: ψ = ψ0 in the presence of a nuisance parameter β, priors under the null and alternative hypotheses must be chosen. As in Bayesian estimation, an
On the use of non‐local prior densities in Bayesian hypothesis tests
Summary.  We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes
Scales of Evidence for Model Selection: Fisher versus Jeffreys
TLDR
A general interpretation of Fisher's scale in terms of Bayes factors is given which works fine when checked for the onedimensional Gaussian problem, where standard hypothesis testing is seen to coincide with a Bayesian analysis that assumes stronger (more informative) priors than those used by the BIC.
Estimators of the local false discovery rate designed for small numbers of tests
TLDR
Corrections of maximum likelihood estimators of the local false discovery rate (LFDR) of histogram-based empirical Bayes methods are introduced and it is found that HBE requires N to be at least 6-12 features to perform as well as the estimators proposed here, with the precise minimum N depending on p0 and dalt.
On the Probability of Observing Misleading Statistical Evidence
Abstract The law of likelihood explains how to interpret statistical data as evidence. Specifically, it gives to the discipline of statistics a precise and objective measure of the strength of
Ancillaries and Conditional Inference
Sufficiency has long been regarded as the primary reduction pro- cedure to simplify a statistical model, and the assessment of the procedure involves an implicit global repeated sampling principle.
Estimating the Null Distribution to Adjust Observed Confidence Levels for Genome‐Scale Screening
TLDR
In a generic simulation study of genome-scale multiple testing, conditioning the observed confidence level on the estimated null distribution as an approximate ancillary statistic markedly improved conditional inference, indicating that estimation of the null distribution tends to exacerbate the conservative bias that results from modeling heavy-tailed data distributions with the normal family.
Asymptotic Properties of Adaptive Likelihood Weights by Cross-Validation
Many versions of weighted likelihood have been studied in the literature. The weighted likelihood that we are interested in was introduced to embrace formally a variety of statistical procedures that
The Intrinsic Bayes Factor for Model Selection and Prediction
TLDR
This article introduces a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual Bayes factors.
...
...