Model fusion and multiple testing in the likelihood paradigm: shrinkage and evidence supporting a point null hypothesis

References

• Wasserstein RL, Lazar NA. The ASA's statement on p-values: context, process, and purpose. Am Stat. 2016;70(2):129–133. doi: 10.1080/00031305.2016.1154108
   Web of Science ®Google Scholar
• Royall R. Statistical evidence: a likelihood paradigm. New York: CRC Press; 1997.
   Google Scholar
• Bickel DR. The strength of statistical evidence for composite hypotheses: inference to the best explanation. Stat Sin. 2012;22:1147–1198.
   Web of Science ®Google Scholar
• Zhang Z, Zhang B. A likelihood paradigm for clinical trials (with discussion). J Stat Theory Pract. 2013;7:157–203. doi: 10.1080/15598608.2013.771545
   Google Scholar
• Alba R, Payton P, Fei Z, et al. Transcriptome and selected metabolite analyses reveal multiple points of ethylene control during tomato fruit development. Plant Cell. 2005;17:2954–2965. doi: 10.1105/tpc.105.036053
   PubMed Web of Science ®Google Scholar
• Bickel DR. Game-theoretic probability combination with applications to resolving conflicts between statistical methods. Int J Approx Reason. 2012;53:880–891. doi: 10.1016/j.ijar.2012.04.002
   Web of Science ®Google Scholar
• Bickel DR, Rahal A. Correcting false discovery rates for their bias toward false positives. Commun Stat Simul Comput. 2019. doi:10.1080/03610918.2019.1630432.
   PubMed Web of Science ®Google Scholar
• Dudoit S, van der Laan MJ. Multiple testing procedures with applications to genomics. New York: Springer; 2008.
   Google Scholar
• Bickel DR. Small-scale inference: empirical Bayes and confidence methods for as few as a single comparison. Int Stat Rev. 2014;82:457–476. doi: 10.1111/insr.12064
   Web of Science ®Google Scholar
• Korn EL, Freidlin B. The likelihood as statistical evidence in multiple comparisons in clinical trials: no free lunch. Biometrical J. 2006;48:346–355. doi: 10.1002/bimj.200510216
   PubMed Web of Science ®Google Scholar
• Strug LJ, Hodge SE. An alternative foundation for the planning and evaluation of linkage analysis I. Decoupling 'error probabilities' from 'measures of evidence'. Hum Hered. 2006;61:166–188. doi: 10.1159/000094709
   PubMed Web of Science ®Google Scholar
• Lindsey J. Parametric statistical inference. Oxford: Oxford Science Publications, Clarendon Press; 1996.
   Google Scholar
• Ando T. Bayesian model selection and statistical modeling. Statistics: a series of textbooks and monographs. Taylor & Francis; 2010
   Google Scholar
• Bickel DR. Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priors. Int J Approx Reason. 2015;66:53–72. doi: 10.1016/j.ijar.2015.07.012
   Web of Science ®Google Scholar
• Bickel DR. A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models. Commun Stat Theory Methods. 2018;47:3125–3137. doi: 10.1080/03610926.2017.1348522
   Web of Science ®Google Scholar
• Claeskens G, Hjort NL. Model selection and model averaging. Cambridge: Cambridge University Press; 2008.
   Google Scholar
• Wasserman L. Bayesian model selection and model averaging. J Math Psychol. 2000;44(1):92–107. doi: 10.1006/jmps.1999.1278
   PubMed Web of Science ®Google Scholar
• Giang PH, Shenoy PP. Decision making on the sole basis of statistical likelihood. Artif Intell. 2005;165:137–163. doi: 10.1016/j.artint.2005.03.004
   Web of Science ®Google Scholar
• Barndorff-Nielsen OE. Adjusted versions of profile likelihood and directed likelihood, and extended likelihood. J R Stat Soc B. 1994;56:125–140.
   Google Scholar
• Bjørnstad JF. On the generalization of the likelihood function and the likelihood principle. J Am Stat Assoc. 1996;91:791–806.
   Web of Science ®Google Scholar
• Pawitan Y. In all likelihood: statistical modeling and inference using likelihood. Oxford: Clarendon Press; 2001.
   Google Scholar
• Wang Z, Klir GJ. Generalized measure theory (IFSR international series on systems science and engineering). New York: Springer; 2008.
   Google Scholar
• Spohn W. The laws of belief: ranking theory and its philosophical applications. Oxford: Oxford University Press; 2012.
   Google Scholar
• Puhalskii A. Large deviations and idempotent probability. Monographs and surveys in pure and applied mathematics. New York: CRC Press; 2001.
   Google Scholar
• Bickel DR. The sufficiency of the evidence, the relevancy of the evidence, and quantifying both with a single number; 2019. Working paper, doi:10.5281/zenodo.2538412.
   Google Scholar
• Severini T. Likelihood methods in statistics. Oxford: Oxford University Press; 2000.
   Google Scholar
• Bickel DR. Pseudo-likelihood, explanatory power, and Bayes's theorem [comment on “A likelihood paradigm for clinical trials”]. J Stat Theory Pract. 2013;7:178–182. doi: 10.1080/15598608.2013.771546
   Google Scholar
• Bickel DR. A predictive approach to measuring the strength of statistical evidence for single and multiple comparisons. Can J Stat. 2011;39:610–631. doi: 10.1002/cjs.10109
   Web of Science ®Google Scholar
• Westfall PH. Comment on B. Efron, “Correlated z-values and the accuracy of large-scale statistical estimates”. J Am Stat Assoc. 2010;105:1063–1066. doi: 10.1198/jasa.2010.tm10239
   Web of Science ®Google Scholar
• Lindley DV. A statistical paradox. Biometrika. 1957;44:187–192. doi: 10.1093/biomet/44.1-2.187
   Web of Science ®Google Scholar
• Efron B. Rejoinder to comments on B. Efron, “Correlated z-values and the accuracy of large-scale statistical estimates”. J Am Stat Assoc. 2010;105:1067–1069. doi: 10.1198/jasa.2010.tm10367
   Web of Science ®Google Scholar
• Bickel DR. Genomics data analysis: false discovery rates and empirical Bayes methods. New York: Chapman and Hall/CRC; 2020. Available from: https://davidbickel.com/genomics/.
   Google Scholar
• Bickel DR. Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing. Stat Methods Appt. 2015;24:523–546. doi: 10.1007/s10260-015-0299-6
   Web of Science ®Google Scholar
• Bickel DR. Confidence distributions applied to propagating uncertainty to inference based on estimating the local false discovery rate: a fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases. Commun Stat Theory Methods. 2017;46:10788–10799. doi: 10.1080/03610926.2016.1248781
   Web of Science ®Google Scholar
• Padilla M, Bickel DR. Estimators of the local false discovery rate designed for small numbers of tests. Stat Appl Genet Mol Biol. 2012;11(5):art. 4. doi: 10.1515/1544-6115.1807
   Web of Science ®Google Scholar
• Yang Y, Aghababazadeh FA, Bickel DR. Parametric estimation of the local false discovery rate for identifying genetic associations. IEEE/ACM Trans Comput Biol Bioinf. 2013;10:98–108. doi: 10.1109/TCBB.2012.140
   PubMed Web of Science ®Google Scholar
• Muralidharan O. An empirical Bayes mixture method for effect size and false discovery rate estimation. Ann Appl Stat. 2010;4:422–438. doi: 10.1214/09-AOAS276
   Web of Science ®Google Scholar
• Pawitan Y, Murthy K, Michiels S, Ploner A. Bias in the estimation of false discovery rate in microarray studies. Bioinformatics. 2005;21:3865–3872. doi: 10.1093/bioinformatics/bti626
   PubMed Web of Science ®Google Scholar
• Karimnezhad A, Bickel DR. Incorporating prior knowledge about genetic variants into the analysis of genetic association data: an empirical Bayes approach. IEEE/ACM Trans Comput Biol Bioinf. 2018. doi:10.1109/TCBB.2018.2865420. Available from: https://ieeexplore.ieee.org/document/8436435/.
   PubMedGoogle Scholar
• Bickel DR. Sharpen statistical significance: evidence thresholds and Bayes factors sharpened into Occam's razor. Stat. 2019;8(1):e215. doi: 10.1002/sta4.215
   Google Scholar
• Held L, Ott M. How the maximal evidence of p-values against point null hypotheses depends on sample size. Am Stat. 2016;70(4):335–341. doi: 10.1080/00031305.2016.1209128
   Web of Science ®Google Scholar
• Jeffreys H. Theory of probability. London: Oxford University Press; 1948.
   Google Scholar
• Benjamin DJ, Berger JO, Johannesson M, et al. Redefine statistical significance. Nat Hum Behav. 2017;1: 0–0.
   Google Scholar
• Bickel DR, Patriota AG. Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters. Bernoulli. 2019;25(1):47–74. doi: 10.3150/17-BEJ942
   Web of Science ®Google Scholar
• Efron B. Large-scale simultaneous hypothesis testing: the choice of a null hypothesis. J Am Stat Assoc. 2004;99:96–104. doi: 10.1198/016214504000000089
   Web of Science ®Google Scholar
• Efron B. Large-Scale inference: empirical Bayes methods for estimation, testing, and prediction. Cambridge: Cambridge University Press; 2010.
   Google Scholar
• Rubin DB. Estimation in parallel randomized experiments. J Educ Stat. 1981;6:377–401. doi: 10.3102/10769986006004377
   Google Scholar