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Archive for the ‘empirical Bayes’ Category

Estimates of the local false discovery rate based on prior information: Application to GWAS

1 August 2016 Comments off

Empirical Bayes single-comparison procedure

1 July 2016 Comments off

D. R. Bickel, “Small-scale inference: Empirical Bayes and confidence methods for as few as a single comparison,” International Statistical Review 82, 457-476 (2014). Published version2011 preprint | Simple explanation (link added 21 June 2017)

Parametric empirical Bayes methods of estimating the local false discovery rate by maximum likelihood apply not only to the large-scale settings for which they were developed, but, with a simple modification, also to small numbers of comparisons. In fact, data for a single comparison are sufficient under broad conditions, as seen from applications to measurements of the abundance levels of 20 proteins and from simulation studies with confidence-based inference as the competitor.

Adaptively selecting an empirical Bayes reference class

1 June 2016 Comments off

F. A. Aghababazadeh, M. Alvo, and D. R. Bickel, “Estimating the local false discovery rate via a bootstrap solution to the reference class problem,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/34295 (2016). 2016 preprint

Categories: empirical Bayes, preprints

Empirical Bayes software (R packages)

1 May 2016 Comments off
Categories: empirical Bayes, software

False discovery rates are misleadingly low

2 March 2016 Comments off

D. R. Bickel, “Correcting false discovery rates for their bias toward false positives,” Working Paper, University of Ottawa, deposited in uO Research at https://goo.gl/GcUjJe (2016). 2016 preprint | Slides: CFDR and RFDR for SSC 2017

12 June 2017: URL updated and slides added

 

Inference after checking the prior & sampling model

1 September 2015 Comments off

D. R. Bickel, “Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priors,” International Journal of Approximate Reasoning 66, 53–72 (2015). Simple explanation | Published version2014 preprint | Slides

S0888613X

The proposed procedure combines Bayesian model checking with robust Bayes acts to guide inference whether or not the model is found to be inadequate:

  1. The first stage of the procedure checks each model within a large class of models to determine which models are in conflict with the data and which are adequate for purposes of data analysis.
  2. The second stage of the procedure applies distribution combination or decision rules developed for imprecise probability.

This proposed procedure is illustrated by the application of a class of hierarchical models to a simple data set.

The link Simple explanation was added on 6 June 2017.

Maximum entropy over a set of posteriors

10 August 2015 Comments off

D. R. Bickel, “Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing,” Statistical Methods & Applications 24, 523-546 (2015). Published article2012 preprint | 2011 preprint | Slides

SMA

This framework of statistical inference facilitates the development of new methodology to bridge the gap between the frequentist and Bayesian theories. As an example, a simple and practical method for combining p-values with a set of possible posterior probabilities is provided.

In this general approach, Bayesian inference is used when the prior distribution is known, frequentist inference is used when nothing is known about the prior, and both types of inference are blended according to game theory when the prior is known to be a member of some set. (The robust Bayes framework represents knowledge about a prior in terms of a set of possible priors.) If the benchmark posterior that corresponds to frequentist inference lies within the set of Bayesian posteriors derived from the set of priors, then the benchmark posterior is used for inference. Otherwise, the posterior within that set that minimizes the cross entropy to the benchmark posterior is used for inference.