# Model Selection confidence sets by likelihood ratio testing

@article{Zheng2019ModelSC, title={Model Selection confidence sets by likelihood ratio testing}, author={Chao Zheng and Davide Ferrari and Yuhong Yang}, journal={Statistica Sinica}, year={2019} }

The traditional activity of model selection aims at discovering a single model superior to other candidate models. In the presence of pronounced noise, however, multiple models are often found to explain the same data equally well. To resolve this model selection ambiguity, we introduce the general approach of model selection confidence sets (MSCSs) based on likelihood ratio testing. A MSCS is defined as a list of models statistically indistinguishable from the true model at a user-specified…

## 11 Citations

### Enhancing Multi-model Inference with Natural Selection

- Computer Science
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The convergence properties of genetic algorithm (GA) are studied based on the Markov chain theory and used to design an adaptive termination criterion that vastly reduces the computational cost.

### Order selection with confidence for finite mixture models

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The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing principle leads to…

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This article first identifies two nested graphical models—called small and large confidence graphs (SCG and LCG)—trapping the true graphical model in between at a given level of confidence, just like the endpoints of traditional confidence interval capturing the population parameter.

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Two simple measures of uncertainty for a model selection procedure are developed, similar in spirit to confidence set in parameter estimation; the second measure is focusing on error in model selection.

### Assessing the Global and Local Uncertainty of Scientific Evidence in the Presence of Model Misspecification

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Non-parametric bootstrap methodologies for estimating the sampling distribution of the evidence estimator under model misspecification are developed, which allows us to determine how secure the authors are in their evidential statement.

### Subdata selection algorithm for linear model discrimination

- Computer ScienceStatistical Papers
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This work proposes a subdata selection method based on leverage scores which enables us to conduct the selection task on a small subdata set and improves the probability of selecting the best model but also enhances the estimation efficiency.

### Ranking the importance of genetic factors by variable‐selection confidence sets

- BiologyJournal of the Royal Statistical Society: Series C (Applied Statistics)
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This work addresses the ambiguity related to SNP selection by constructing a list of models—called a variable‐selection confidence set (VSCS)—which contains the collection of all well‐supported SNP combinations at a user‐specified confidence level.

### Discussion on Prior-based Bayesian Information Criterion (PBIC) by M. J. Bayarri, James O. Berger, Woncheol Jang, Surajit Ray, Luis R. Pericchi, and Ingmar Visser

- Computer ScienceStatistical Theory and Related Fields
- 2019

This elucidating paper unpacked a dangerous complication when one takes the classic BIC verbatim as an approximation to themarginal likelihood, and proposed the Prior-based Bayesian Information Criterion (PBIC) as a principled correction.

### Variable Importance Based Interaction Modeling with an Application on Initial Spread of COVID-19 in China (preprint)

- Computer Science
- 2022

This paper introduces a variable importance based interaction modeling (VIBIM) procedure for learning interactions in a linear regression model with both continuous and categorical predictors and shows that the VIBIM approach leads to better models in terms of interpretability, stability, reliability and prediction.

### Visualization and assessment of model selection uncertainty

- Computer ScienceComputational Statistics & Data Analysis
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