Biostatistics Virtual Seminar - Dr. Joe Cavanaugh on Probabilistic Pairwise Model Comparisons
When & Where
March 21, 2023
12:00 PM - 1:00 PM
Contact
- Scott Dyson
- scott.b.dyson@uth.tmc.edu
Event Description
Presenter:
Joe Cavanaugh, Ph.D.
Professor, Head of the Department of Biostatistics at the University of Iowa.
Abstract:
In problems involving the selection and assessment of statistical models, discrepancy measures are often employed. A discrepancy gauges the separation between a fitted candidate model and the underlying generating model. In this work, we consider pairwise comparisons of fitted models based on a probabilistic evaluation of the ordering of the constituent discrepancies. An estimator of the probability is derived using the nonparametric bootstrap.
In the framework of hypothesis testing, nested models are often compared on the basis of the p-value. Specifically, the simpler null model is favored unless the p-value is sufficiently small, in which case the null model is rejected and the more general alternative model is retained. We argue that in certain settings, the p-value and the bootstrap discrepancy comparison probability (BDCP) are equivalent. In particular, we have established this equivalence for the Wald, score, and likelihood ratio tests by employing suitably defined discrepancy measures.
We contend that the connection between the p-value and the BDCP not only leads to potentially new insights regarding the utility and limitations of the p-value, yet also facilitates discrepancy-based inferences in settings beyond the restricted confines of hypothesis testing. In particular, the development of the BDCP does not assume that either the null or alternative model represents the truth, yet rather evaluates the optimality of the fitted models based on the bias/variability tradeoff. The use of the BDCP does not require nested models or large sample sizes. Moreover, a simple refinement of the BDCP provides a probabilistic measure that not only leans towards zero when the alternative model is optimal, yet also leans towards one when the null model is optimal.
This work is joint with Andres Dajles, Ben Riedle, and Andrew Neath.
WebEx Password:
3pF3pYPWZx6
Event Site Link
https://uthealth.webex.com/uthealth/j.php?MTID=m113cf3cbcba643b4307425b638be93e6
Additional Information
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Presenter:
Joe Cavanaugh, Ph.D.
Professor, Head of the Department of Biostatistics at the University of Iowa.
Abstract:
In problems involving the selection and assessment of statistical models, discrepancy measures are often employed. A discrepancy gauges the separation between a fitted candidate model and the underlying generating model. In this work, we consider pairwise comparisons of fitted models based on a probabilistic evaluation of the ordering of the constituent discrepancies. An estimator of the probability is derived using the nonparametric bootstrap.
In the framework of hypothesis testing, nested models are often compared on the basis of the p-value. Specifically, the simpler null model is favored unless the p-value is sufficiently small, in which case the null model is rejected and the more general alternative model is retained. We argue that in certain settings, the p-value and the bootstrap discrepancy comparison probability (BDCP) are equivalent. In particular, we have established this equivalence for the Wald, score, and likelihood ratio tests by employing suitably defined discrepancy measures.
We contend that the connection between the p-value and the BDCP not only leads to potentially new insights regarding the utility and limitations of the p-value, yet also facilitates discrepancy-based inferences in settings beyond the restricted confines of hypothesis testing. In particular, the development of the BDCP does not assume that either the null or alternative model represents the truth, yet rather evaluates the optimality of the fitted models based on the bias/variability tradeoff. The use of the BDCP does not require nested models or large sample sizes. Moreover, a simple refinement of the BDCP provides a probabilistic measure that not only leans towards zero when the alternative model is optimal, yet also leans towards one when the null model is optimal.
This work is joint with Andres Dajles, Ben Riedle, and Andrew Neath.
WebEx Password:
3pF3pYPWZx6
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