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Watanabe-Akaike information criterion (WAIC; Watanabe, 2010) and leave-one-out cross validation (LOO) are two fully Bayesian model selection methods that have been shown to perform better than other traditional information-criterion based…

Applications · Statistics 2018-06-27 Luo Yong

Model inference, such as model comparison, model checking, and model selection, is an important part of model development. Leave-one-out cross-validation (LOO) is a general approach for assessing the generalizability of a model, but…

Machine Learning · Statistics 2020-08-12 Måns Magnusson , Michael Riis Andersen , Johan Jonasson , Aki Vehtari

Bayesian diagnostic classification models (Bayesian DCMs) are effective for diagnosing students' skills. Research on the evaluation of relative model fit indices for DCMs using Bayesian estimation, however, is deficient. This study…

Applications · Statistics 2024-10-07 Ae Kyong Jung , Jonathan Templin

Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the…

Computation · Statistics 2023-09-28 Luca Silva , Giacomo Zanella

A natural method for approximating out-of-sample predictive evaluation is leave-one-out cross-validation (LOOCV) --- we alternately hold out each case from a full data set and then train a Bayesian model using Markov chain Monte Carlo…

Methodology · Statistics 2017-04-28 Longhai Li , Shi Qiu , Bei Zhang , Cindy X. Feng

Recently, new methods for model assessment, based on subsampling and posterior approximations, have been proposed for scaling leave-one-out cross-validation (LOO) to large datasets. Although these methods work well for estimating predictive…

Methodology · Statistics 2020-08-12 Måns Magnusson , Michael Riis Andersen , Johan Jonasson , Aki Vehtari

Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of…

Applications · Statistics 2020-05-28 Riko Kelter

In recent decades, multilevel regression and poststratification (MRP) has surged in popularity for population inference. However, the validity of the estimates can depend on details of the model, and there is currently little research on…

Methodology · Statistics 2022-09-07 Swen Kuh , Lauren Kennedy , Qixuan Chen , Andrew Gelman

It is useful to estimate the expected predictive performance of models planned to be used for prediction. We focus on leave-one-out cross-validation (LOO-CV), which has become a popular method for estimating predictive performance of…

Methodology · Statistics 2025-10-29 Tuomas Sivula , Måns Magnusson , Asael Alonzo Matamoros , Aki Vehtari

We present a weighted version of Leave-One-Out (LOO) cross-validation for estimating the Integrated Squared Error (ISE) when approximating an unknown function by a predictor that depends linearly on evaluations of the function over a finite…

Machine Learning · Statistics 2025-05-27 Luc Pronzato , Maria-João Rendas

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the…

Computation · Statistics 2016-08-09 Aki Vehtari , Tommi Mononen , Ville Tolvanen , Tuomas Sivula , Ole Winther

Cross-validation can be used to measure a model's predictive accuracy for the purpose of model comparison, averaging, or selection. Standard leave-one-out cross-validation (LOO-CV) requires that the observation model can be factorized into…

Methodology · Statistics 2021-06-21 Paul-Christian Bürkner , Jonah Gabry , Aki Vehtari

In many real-world applications, we are interested in approximating black-box, costly functions as accurately as possible with the smallest number of function evaluations. A complex computer code is an example of such a function. In this…

Computation · Statistics 2022-03-22 Hossein Mohammadi , Peter Challenor , Daniel Williamson , Marc Goodfellow

One of the common goals of time series analysis is to use the observed series to inform predictions for future observations. In the absence of any actual new data to predict, cross-validation can be used to estimate a model's future…

Methodology · Statistics 2020-07-02 Paul-Christian Bürkner , Jonah Gabry , Aki Vehtari

The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as $K$-fold cross validation suffer from large biases. Motivated by the low bias of the leave-one-out cross…

Methodology · Statistics 2020-02-12 Kamiar Rahnama Rad , Arian Maleki

We consider predictive checking for Bayesian model assessment using leave-one-out probability integral transform (LOO-PIT). LOO-PIT values are conditional cumulative predictive probabilities given LOO predictive distributions and…

Methodology · Statistics 2026-05-14 Herman Tesso , Aki Vehtari

In this paper we consider the problem of Gaussian process classifier (GPC) model selection with different Leave-One-Out (LOO) Cross Validation (CV) based optimization criteria and provide a practical algorithm using LOO predictive…

Machine Learning · Computer Science 2012-06-27 Sundararajan Sellamanickam , Sathiya Keerthi Selvaraj

In the field of spatial data analysis, spatially varying coefficients (SVC) models, which allow regression coefficients to vary by region and flexibly capture spatial heterogeneity, have continued to be developed in various directions.…

Methodology · Statistics 2025-10-14 Yuko Kakikawa , Yoshiyuki Ninomiya

Recursive partitioning approaches producing tree-like models are a long standing staple of predictive modeling, in the last decade mostly as ``sub-learners'' within state of the art ensemble methods like Boosting and Random Forest. However,…

Machine Learning · Statistics 2015-12-14 Amichai Painsky , Saharon Rosset

The out-of-sample error (OO) is the main quantity of interest in risk estimation and model selection. Leave-one-out cross validation (LO) offers a (nearly) distribution-free yet computationally demanding approach to estimate OO. Recent…

Statistics Theory · Mathematics 2023-10-27 Arnab Auddy , Haolin Zou , Kamiar Rahnama Rad , Arian Maleki
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