An eScience-Bayes strategy for analyzing omics data

<p>Abstract</p> <p>Background</p> <p>The omics fields promise to revolutionize our understanding of biology and biomedicine. However, their potential is compromised by the challenge to analyze the huge datasets produced. Analysis of omics data is plagued by the curse of dimensionality, resulting in imprecise estimates of model parameters and performance. Moreover, the integration of omics data with other data sources is difficult to shoehorn into classical statistical models. This has resulted in <it>ad hoc </it>approaches to address specific problems.</p> <p>Results</p> <p>We present a general approach to omics data analysis that alleviates these problems. By combining eScience and Bayesian methods, we retrieve scientific information and data from multiple sources and coherently incorporate them into large models. These models improve the accuracy of predictions and offer new insights into the underlying mechanisms. This "eScience-Bayes" approach is demonstrated in two proof-of-principle applications, one for breast cancer prognosis prediction from transcriptomic data and one for protein-protein interaction studies based on proteomic data.</p> <p>Conclusions</p> <p>Bayesian statistics provide the flexibility to tailor statistical models to the complex data structures in omics biology as well as permitting coherent integration of multiple data sources. However, Bayesian methods are in general computationally demanding and require specification of possibly thousands of prior distributions. eScience can help us overcome these difficulties. The eScience-Bayes thus approach permits us to fully leverage on the advantages of Bayesian methods, resulting in models with improved predictive performance that gives more information about the underlying biological system.</p

Improving Bayesian credibility intervals for classifier error rates using maximum entropy empirical priors

Objective: Successful use of classifiers that learn to make decisions from a set of patient examples require robust methods for performance estimation. Recently many promising approaches for determination of an upper bound for the error rate of a single classifier have been reported but the Bayesian credibility interval (CI) obtained from a conventional holdout test still delivers one of the tightest bounds. The conventional Bayesian CI becomes unacceptably large in real world applications where the test set sizes are less than a few hundred. The source of this problem is that fact that the CI is determined exclusively by the result on the test examples. In other words, there is no information at all provided by the uniform prior density distribution employed which reflects complete lack of prior knowledge about the unknown error rate. Therefore, the aim of the study reported here was to study a maximum entropy (ME) based approach to improved prior knowledge and Bayesia n CIs, demonstrating its relevance for biomedical research and clinical practice. Method and material: It is demonstrated how a refined non-uniform prior density distribution can be obtained by means of the ME principle using empirical results from a few designs and tests using non-overlapping sets of examples. Results: Experimental results show that ME based priors improve the CIs when employed to four quite different simulated and two real world data sets. Conclusions: An empirically derived ME prior seems promising for improving the Bayesian CI for the unknown error rate of a designed classifier