|Apr 28, 2017||
Singdhansu Chatterjee, Ph.D.
Model Discovery using Statistical Evaluation Maps
In a typical statistical or data science exercise, both data and a statistical model are involved. While there is often little or no ambiguity about data, there can be many alternatives about how to analyze such data, and how to interpret the results. We recognize various possible transformations of the data, different model fitting algorithms, practical safeguards put in place to ensure robustness and sensitivity balance in the results, different methods of data analysis, different statistical paradigms of interpretation of results, as all equally deserving to be considered as crucial components of a statistical model. We present method for evaluating the performance of different, potentially incomparable, models. In the context of the classical problem of variable or covariate selection, our proposed method leads to an algorithm where only one model needs to be fitted to data to elicit all variables of interest. Our resampling-based approach allows for simultaneous model selection and approximation of sampling distribution of consistent estimators under any model. We demonstrate the performance of our proposal with simulation experiments, and real examples on climate and neuroscience data modeling.
This work is joint with my student Subhabrata Majumdar at the University of Minnesota.
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