## Assessing multiple models

D. R. Bickel, “Inference after checking multiple Bayesian models for data conflict,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/1039/31135 (2014). 2014 preprint | Slides

## MLE of the local FDR

Y. Yang, F. A. Aghababazadeh, and D. R. Bickel, “Parametric estimation of the local false discovery rate for identifying genetic associations,” *IEEE/ACM Transactions on Computational Biology and Bioinformatics* **10**, 98-108 (2013). 2010 version | Slides

## Bayes/non-Bayes blended inference

Updated with a new multiple comparison procedure and applications on 30 June 2012 and with slides for a presentation on 5 October 2012:

D. R. Bickel, “Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/23124 (2012). 2012 preprint | 2011 preprint | Slides

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 new approach to statistics, 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 is closest to the benchmark posterior is used for inference.

## How to combine statistical methods

D. R. Bickel, “Game-theoretic probability combination with applications to resolving conflicts between statistical methods,” *International Journal of Approximate Reasoning* **53**, 880-891 (2012). Full article | 2011 preprint | Slides | Simple explanation

This paper proposes both a novel solution to the problem of combining probability distributions and a framework for using the new method to combine the results of differing statistical methods that may legitimately be used to analyze the same data set. While the paper emphasizes theoretical development, it is motivated by the need to combine two conflicting estimators of the probability of differential gene expression.

## Information-theoretic analysis of -omics data

To view the slides and plots of the lecture “Information-theoretic analysis of -omics data,” delivered 17 November 2008 in BIO 5106 (BIOL 5506) Bioinformatics, follow this link and select “Download.” The slides are also available separately.

Corrected 16 January 2009.

License: Attribution Non-commercial.

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