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Understanding predictive information criteria for Bayesian models
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“Although information criteria are computationally convenient, they are based on asymptotic results and assumptions about the data that may not always hold [89].”
From Comparing Bayesian and non-Bayesian accounts of human confidence reports (2018) · cites this paper as [89]
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“WAIC is a more Bayesian approach to information criteria that adds a correction for the effective number of parameters [89].”
From Comparing Bayesian and non-Bayesian accounts of human confidence reports (2018) · cites this paper as [89]
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“There is also something called the Bayesian information criterion (a misleading name, we believe) that adjusts for the number of fitted parameters with a penalty that increases with the sample size, n (Schwarz 1978).”
BackgroundModel selection and multimodel inference: a practical information-theoretic approach.
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“The log predictive density has an important role in statistical model comparison because of its connection to the Kullback-Leibler information measure (see Burnham and Anderson, 2002, and Robert, 1996).”
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“In this asymptotic limit, the posterior is dominated by the likelihood—the prior contributes only one factor, while the likelihood contributes n factors, one for each data point—and so the likelihood function also approaches the same normal distribution.”
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“When several candidate models are available, they can be compared and averaged using Bayes factors (which is equivalent to embedding them in a larger discrete model) or some more practical approximate procedure (Hoeting et al., 1999) or continuous model expansion (Draper, 1999).”
MethodInformation Theory and an Extension of the Maximum Likelihood Principle
Akaike, H. (1992) · Springer Series in Statistics · doi:10.1007/978-1-4612-0919-5_38 · Cited by 3,028 · cited 5×
“For practical reasons alone, there remains a place for simple bias corrections such as AIC (Akaike, 1973), DIC (Spiegelhalter et al., 2002, van der Linde, 2005), and, more recently, WAIC (Watanabe, 2010), and all these can be viewed as approximations to different versions of cross-validation (Stone,…”
BackgroundMethodInfluentialWatanabe, S. (2010) · Journal of machine learning research · doi:10.5555/1756006.1953045 · Cited by 2,921 · cited 5×
“Bayesian cross-validation works also with singular models, and Bayesian LOO-CV has been proven to asymptotically equal to WAIC (Watanabe, 2010).”
BackgroundMethodInfluentialBayesian Data Analysis, 2nd edn
Brix, A. (2005) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2004.00347_4.x · Cited by 2,588 · cited 3×
“As is well known in hierarchical modeling (see, e.g., Spiegelhalter et al. 2002; Gelman et al. 2003), the line separating prior distribution from likelihood is somewhat arbitrary and is related to the question of what aspects of the data will be changed in hypothetical replications.”
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Albrecht, L., & Kaufeld, K. (2023) · Frontiers in Public Health · doi:10.3389/fpubh.2023.1100543 · Cited by 12
“predictive accuracy which adds a correction for the effective number of parameters to adjust for overfitting (38, 39).”
BackgroundGashu, C., Marine, B. T., Alemu, C., & Kassa, Y. (2023) · BMC Women s Health · doi:10.1186/s12905-023-02202-9 · Cited by 11
“A different option is the Watanabe Akaike Information Criteria (WAIC) [28], which develops a criterion using a more thoroughly Bayesian methodology [14].”
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Should I stay or should I go: factors influencing mate retention and divorce in a colonial seabird
Wagner, E. L., Cappello, C. D., & Boersma, P. D. (2022) · Animal Behaviour · doi:10.1016/j.anbehav.2022.08.002 · Cited by 17
Boggio-Pasqua, A., Kim, B.-H., Aeberhard, W. H., Hoopes, L. A., Swider, D. A., Wilkinson, K., & Dureuil, M. (2022) · Frontiers in Marine Science · doi:10.3389/fmars.2022.960822 · Cited by 12
“This posterior distribution is not available in a closed form here, thus we relied on the No-U-Turn Sampling (NUTS) algorithm (Hoffman and Gelman, 2014) which can be considered as an advanced Markov chain Monte Carlo (MCMC) method.”
MethodMathematical theory of Bayesian statistics for unknown information source
Watanabe, S. (2023) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2022.0151 · Cited by 13
“If a leverage sample point is contained in a sample, the posterior average or variance may be infinite [42,43], and a new estimation method has been proposed, which is useful in many practical problems [12,13,44,45].”
MethodDey, S., Moqanaki, E. M., Milleret, C., Dupont, P., Tourani, M., & Bischof, R. (2022) · bioRxiv · doi:10.1101/2022.05.12.491684 · Cited by 12
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Two-step mixed-type multivariate Bayesian sparse variable selection with shrinkage priors
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Within city spatiotemporal variation of pollen concentration in the city of Toronto, Canada.
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The impact of sleep loss on decision making: Opening the cognitive black box
Lim, J. Y. L., Killgore, W. D. S., Bennett, D., & Drummond, S. P. A. (2025) · Sleep Medicine Reviews · doi:10.1016/j.smrv.2025.102114 · Cited by 16
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Bayesian inference: more than Bayes’s theorem
Loredo, T., & Wolpert, R. L. (2024) · Frontiers in Astronomy and Space Sciences · doi:10.3389/fspas.2024.1326926 · Cited by 11
“For a Bayesian perspective on model selection relying on measures of anticipated out-of-sample predictive performance (vs. a prior prediction of the observed sample, as measured by marginal likelihood), see Gelman et al. (2014b).”
BackgroundbayesTPC: Bayesian inference for Thermal Performance Curves in R
Sorek, S., Smith, J. W., Huxley, P. J., & Johnson, L. R. (2024) · bioRxiv · doi:10.1111/2041-210x.70004 · Cited by 11
A Hierarchical Model for eDNA Fate and Transport Dynamics Accommodating Low Concentration Samples
Augustine, B. C., Hutchins, P., Jones, D. N., Williams, J. R., Leinonen, E., & Sepulveda, A. J. (2024) · bioRxiv · doi:10.1007/s10651-024-00632-8 · Cited by 11
“To compare the inhibitor models to the null models, we used posterior predictive checks (Gelman et al. 1996; Conn et al. 2018) and the conditional Watanabe–Akaike Information Criterion (WAIC; Watanabe and Opper 2010; Gelman et al. 2014).”
Proximity to rewards modulates parameters of effortful control exertion.
Devine, S., Roy, M., Beierholm, U., & Otto, A. R. (2024) · Journal of Experimental Psychology General · doi:10.1037/xge0001561 · Cited by 13
“Accordingly, we fi t 2,744 separate HDDMs to the data, which covered the full model and parameter space, and compared model fi t for each model using the deviance information criterion (DIC; Gelman et al., 2014).”
MethodComparing the performance of two camera trap-based methods to survey small mustelids
Barros, A. L., Marques, M., Alcobia, S., MacKenzie, D. I., & Santos-Reis, M. (2024) · Basic and Applied Ecology · doi:10.1016/j.baae.2024.01.004 · Cited by 11
Yin, Z., Zhang, C., Fan, X., Zhang, N.-L., Zhao, X.-H., & von Gadow, K. (2023) · Forest Ecology and Management · doi:10.1016/j.foreco.2023.121234 · Cited by 11
Mammalian resistance to megafire in western U.S. woodland savannas
Calhoun, K., Goldstein, B. R., Gaynor, K., McInturff, A., Solorio, L., & Brashares, J. (2023) · Ecosphere · doi:10.1002/ecs2.4613 · Cited by 11
“…” covariate, we fit the community multispecies occupancy model using each of the burn category parameterizations and compared their Watanabe – Akaike information criterion (WAIC) values (Gelman et al., 2014), using the WAIC function from the nimble package in R (v.0.11.1) (de Valpine et al., 2017).”
MethodInfluentialBayesian estimation of covariate assisted principal regression for brain functional connectivity
Park, H. (2024) · Biostatistics · doi:10.1093/biostatistics/kxae023 · Cited by 6
Bayesian temporal, spatial and spatio-temporal models of dengue in a small area with INLA
Sani, A., Abapihi, B., Mukhsar, Tosepu, R., Usman, I., & Rahman, G. A. (2022) · International Journal of Modelling and Simulation · doi:10.1080/02286203.2022.2139108 · Cited by 11
“Our primary measures in the model selection are the standard Deviance Information Criterion (DIC) [29] and the Watanabe–Akaike Information Criterion (WAIC) [30,31].”
MethodHigh-dimensional order-free multivariate spatial disease mapping
Fuenzalida, G. V., Adín, A., Goicoa, T., & Ugarte, M. D. (2023) · Statistics and Computing · doi:10.1007/s11222-023-10263-x · Cited by 13
Discovering Online Shopping Preference Structures in Large and Frequently Changing Store Assortments
Kim, M., & Zhang, J. (2022) · Journal of Marketing Research · doi:10.1177/00222437221130722 · Cited by 11
“It is particularly desirable in our context, which involves models with hierarchical and mixture structures, and thus the number of parameters increases with the sample size (Gelman, Hwang, and Vehtari 2014).”
BackgroundGhaderi-Kangavari, A., Rad, J. A., Parand, K., & Nunez, M. D. (2022) · bioRxiv · doi:10.1101/2022.04.07.487571 · Cited by 11
EczemaPred: A computational framework for personalised prediction of eczema severity dynamics
Hurault, G., Stalder, J. F., Méry, S., Delarue, A., Aroman, M. S., Josse, G., & Tanaka, R. J. (2022) · Clinical and Translational Allergy · doi:10.1002/clt2.12140 · Cited by 15
“15 We also computed an accuracy metric for PO ‐ (o)SCORAD predictions, defined as the probability that the predictions were within five units of the measured score.”
MethodMuhammad, I., Wang, X.-G., Li, C.-Y., Yan, M., Mukhtar, M., & Muhammad, M. (2022) · Symmetry · doi:10.3390/sym14020353 · Cited by 11
Understanding the causes and consequences of variability in infant ERP editing practices.
Monroy, C. D., Domínguez-Martínez, E., Taylor, B. M., Marin, O., Parise, E., & Reid, V. (2021) · Developmental Psychobiology · doi:10.1002/dev.22217 · Cited by 11
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“The WAIC is a predictive information criterion that weighs in the prediction accuracy and model complexity (44).”
BackgroundResultInfluentialKuehn, N. M. (2022) · Bulletin of Earthquake Engineering · doi:10.1007/s10518-022-01443-7 · Cited by 11
Ghorbanian, J., Casaprima, N., & Olivier, A. (2024) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2024.117645 · Cited by 10
“Finally, the expected log-pointwise predictive density [40] combines both mean and uncertainty assessment, and can be computed from the ensemble of NNs (with trained weights ˆ ω [ k ] , k = 1 : K ) as: Again, table 3 shows that all metrics improve as the number of training data points increases.”
Gashu, C., & Aguade, A. E. (2024) · BMC Women s Health · doi:10.1186/s12905-024-02954-y · Cited by 8
“By applying the Bayes theorem to the data, the Bayesian techniques integrate information from the data with unbiased prior knowledge [21].”
MethodWang, J., Doogan, N. J., Thompson, K., Bernson, D., Feaster, D. J., Villani, J., Chandler, R. K., White, L. F., Kline, D. M., & Barocas, J. (2023) · Epidemiology · doi:10.1097/ede.0000000000001653 · Cited by 10
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“The predictive performance (ELPD and RMSE) and summed cost of each sub-model were estimated.”
MethodInfluentialBayesian partial pooling to reduce uncertainty in overcoring rock stress estimation
Feng, Y., Gao, K., & Lacasse, S. (2023) · Journal of Rock Mechanics and Geotechnical Engineering · doi:10.1016/j.jrmge.2023.05.003 · Cited by 10
Bayesian CART models for insurance claims frequency
Zhang, Y.-J., Ji, L.-P., Aivaliotis, G., & Taylor, C. C. (2023) · Social Science Research Network · doi:10.48550/arxiv.2303.01923 · Cited by 10
“Note that DIC is defined using plug-in prediction densities More recently, a new criterion called WAIC was introduced by Watababe [51] (see also [49, 50]), where in its definition the plug-in prediction density is replaced by the full When the explicit expression is not available, this posterior…”
MethodTomlinson, S., Lomolino, M. V., Anderson, A., Austin, J., Brown, S. C., Haythorne, S., Perry, G., Wilmshurst, J., Wood, J. R., & Fordham, D. (2023) · bioRxiv · doi:10.1038/s41598-024-55180-9 · Cited by 10
“This POM process was stopped when Bayes factors indicated that the selected posteriors no longer differed from the informed priors 56 .”
BackgroundMethodHan, E.-K., Tamaki, I., Oh, S.-H., Park, J.-S., Cho, W.-B., Jin, D.-P., Kim, B.-Y., Yang, S.-Y., Son, D.-C., Choi, H., et al. (2022) · Annals of Botany · doi:10.1093/aob/mcac142 · Cited by 10
“Using 1000 randomly drawn posteriors, a predictive simulation was carried out, and predictive values were compared with the observed values to confirm the goodnessof-fit of the model to the observed data (Gelman et al., 2014).”
MethodAre you using test log-likelihood correctly?
Deshpande, S. K., Ghosh, S. K., Nguyen, T. D., & Broderick, T. (2022) · Trans. Mach. Learn. Res. · doi:10.48550/arxiv.2212.00219 · Cited by 10
“There are myriad approximate inference algorithms – e.g. Laplace approximation, Hamiltonian Monte Carlo (HMC), mean-field variational inference, to name just a few.”
MethodKerric, A., Mazerolle, M., Giroux, J., & Verreault, J. (2022) · Science of the Total Environment · doi:10.2139/ssrn.4129855 · Cited by 10
An Ordinal Latent Variable Model of Conflict Intensity
Stoehr, N., Hennigen, L. T., Valvoda, J., West, R., Cotterell, R., & Schein, A. (2022) · Annual Meeting of the Association for Computational Linguistics · doi:10.48550/arxiv.2210.03971 · Cited by 10
Simultaneous multifactor Bayesian analysis (SiMBA) of PET time activity curve data
Matheson, G. J., & Ogden, R. T. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119195 · Cited by 9
Masinaei, M. (2022) · International Journal of Biometeorology · doi:10.1007/s00484-022-02263-9 · Cited by 13
“On the other side, WAIC is less often utilized in practice due to the extra computational work required and potential challenges in dealing with structured data (Gelman et al. 2014).”
BackgroundGeographic Variation in Migratory Grasshopper Recruitment under Projected Climate Change
Humphreys, J. M., Srygley, R. B., & Branson, D. (2022) · Geographies · doi:10.3390/geographies2010003 · Cited by 10
“Metrics used for model comparison included the deviance information criterion (DIC), Watanabe–Akaike information criterion (WAIC), and the log-conditional predictive ordinate (lCPO) [84,85].”
MethodAssessing survival time of heart failure patients: using Bayesian approach
Ashine, T., Muleta, G., & Tadesse, K. (2021) · Journal of Big Data · doi:10.1186/s40537-021-00537-4 · Cited by 10
“An alternative is the Watanabe Akaike information criterion (WAIC) [37], which follows a more fully Bayesian approach to construct a criterion [17].”
MethodImpulsivity Relates to Multi-Trial Choice Strategy in Probabilistic Reversal Learning
Zou, A. R., Lopez, D. E. M., Johnson, S. L., & Collins, A. G. E. (2022) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2022.800290 · Cited by 11
“WAIC averages over the posterior distribution instead of conditioning on a point estimate, which is what AIC and BIC condition on, and is thus more appropriate for our hierarchical Bayesian modeling approach (68).”
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Trochta, J., & Branch, T. (2021) · ICES Journal of Marine Science · doi:10.1093/icesjms/fsab165 · Cited by 10
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Bayesian approach to piecewise growth mixture modeling: Issues and applications in school psychology
Heo, I., Depaoli, S. A., Jia, F., & Liu, H. (2024) · Journal of School Psychology · doi:10.1016/j.jsp.2024.101366 · Cited by 9
Evaluation and validation criteria for kinetic models in food science: A critical review
Brahimi, N., Medouni‐Haroune, L., Messaoudene, L., Mouhoubi, K., Remini, H., Allam, A., Brara, Z., Brahimi, Y., Ouchen, A., Negrichi, S., et al. (2024) · Trends in Food Science & Technology · doi:10.1016/j.tifs.2024.104857 · Cited by 12
Brugel, M., Gauthier, V., Bouché, O., Blangiardo, M., & Génin, M. (2024) · European Journal of Epidemiology · doi:10.1007/s10654-024-01176-8 · Cited by 9
“The model with the best fit was chosen as the one minimizing Watanabe-Akaike information criterion (WAIC) [25], a commonly used criterion based on model fit and model complexity.”
Quantifying the spatial spillover effects of non-pharmaceutical interventions on pandemic risk
Wang, K., Han, X., Dong, L., Chen, X., Xiu, G., Kwan, M., & Liu, Y. (2023) · International Journal of Health Geographics · doi:10.1186/s12942-023-00335-6 · Cited by 8
“To determine the value of k, we use the deviance information criterion (DIC) as described in Gelman [40].”
MethodInfluentialFujimoto, K. A., & Falk, C. F. (2023) · Educational and Psychological Measurement · doi:10.1177/00131644231165520 · Cited by 17
“Although the DIC is often the most popular predictive performance index due to its wide availability, there are other recently developed indices that could be used for model selection (Gelman et al., 2014; Vehtari et al., 2017).”
Estimating extreme monthly rainfall for Spain using non-stationary techniques
Urrea-Méndez, D., & del Jesus, M. (2023) · Hydrological Sciences Journal · doi:10.1080/02626667.2023.2193294 · Cited by 9
Gruenewald, P. J., Sumetsky, N., Mair, C., Lee, J. P., & Ponicki, W. R. (2023) · Drug and Alcohol Review · doi:10.1111/dar.13644 · Cited by 11
Identifying historical and future global change drivers that place species recovery at risk
Geary, W. L., Tulloch, A., Ritchie, E., Doherty, T., Nimmo, D., Maxwell, M., & Wayne, A. (2023) · Global Change Biology · doi:10.1111/gcb.16661 · Cited by 9
“The SEM with the lowest WAIC value within a candidate set can be interpreted as being the most parsimonious model, balancing model complexity and the fit of the model to the data (Gelman et al., 2014).”
BackgroundMethodEfficient and Accurate Learning of Mixtures of Plackett-Luce Models
Nguyen, D., & Zhang, A. Y. (2023) · AAAI Conference on Artificial Intelligence · doi:10.48550/arxiv.2302.05343 · Cited by 9
“K is chosen using Bayesian Information Criterion (Gelman, Hwang, and Vehtari 2014) on the validation set and the log-likelihood of the final model is evaluated using the test set.”
MethodMacNab, Y. (2023) · Spatial Statistics · doi:10.1016/j.spasta.2023.100726 · Cited by 9
Shimada, T., Limpus, C., FitzSimmons, N., Ferguson, J., Limpus, D., & Spinks, R. K. (2022) · Regional Environmental Change · doi:10.1007/s10113-022-02014-x · Cited by 9
Recent advances in algebraic geometry and Bayesian statistics
Watanabe, S. (2022) · Information Geometry · doi:10.1007/s41884-022-00083-9 · Cited by 1
“In order to estimate the generalization loss, three random variables are defined, the training loss Tn, the leave-one-out cross validation Cn [15, 38, 18], and the widely applicable information criterion Wn [49] respectively by Tn = − 1 n n”
BackgroundNavigating the Statistical Minefield of Model Selection and Clustering in Neuroscience
Király, B., & Hangya, B. (2022) · eNeuro · doi:10.1523/eneuro.0066-22.2022 · Cited by 12
“Newest in this family, the “ leave one out ” information criterion (LOOIC) is similar to WAIC (Watanabe, 2010b; Gelman et al., 2014; Vehtari et al., 2017; Yong, 2018), but it has been proposed to yield more robust results in the finite case with weak priors or influential observations (Vehtari et…”
BackgroundBayesian time-varying occupancy model for West Nile virus in Ontario, Canada
Temple, S. D., Manore, C. A., & Kaufeld, K. (2022) · Stochastic environmental research and risk assessment (Print) · doi:10.1007/s00477-022-02257-4 · Cited by 9
“For each model, we checked trace plots and the Gelman-Rubin diagnostic (Gelman et al. 2013) to ensure convergence of all regression effects.”
MethodBayesian space-time SIR modeling of Covid-19 in two US states during the 2020–2021 pandemic
Lawson, A., & Kim, J. (2022) · medRxiv · doi:10.1371/journal.pone.0278515 · Cited by 9
“The WAIC is a widely used measure of fit adjusted for the degree of parameterization [14].”
MethodModelling Human Brucellosis Based on Infection Rate and Vaccination Coverage of Sheep and Goats
Dougas, G., Katsiolis, A., Linou, M., Kostoulas, P., & Billinis, C. (2022) · Pathogens · doi:10.3390/pathogens11020167 · Cited by 9
“This can be evaluated by the use of goodness-of-fit tests, which are based on the comparison between the observed data and the predictions under the model [23].”
MethodBayesian regularization for a non-stationary Gaussian linear mixed effects model
Gecili, E., Sivaganesan, S., Asar, O., Clancy, J., Ziady, A., & Szczesniak, R. (2021) · Statistics in Medicine · doi:10.1002/sim.9279 · Cited by 9
“3 (31-172), with an average (range) follow-up time of 15.”
BackgroundBehavioral Strategies and the Spatial Pattern Formation of Nesting
Batsleer, F., Maes, D., & Bonte, D. (2021) · American Naturalist · doi:10.1086/717226 · Cited by 9
Hamer, A. (2021) · Urban Ecosystems · doi:10.1007/s11252-021-01162-y · Cited by 9
Overman, A. A., Stephens, J. D. W., & Bernhardt, M. F. (2021) · Memory · doi:10.1080/09658211.2021.1957937 · Cited by 7
Potential of establishing the universal critical nitrogen dilution curve for drip-irrigated maize
Ma, W., Chen, G., Zhang, X.-Z., Zhang, X.-J., Zhang, C., Li, Z., Su, H., Wang, X., Li, X.-N., & Wei, C.-Z. (2025) · Field crops research (Print) · doi:10.1016/j.fcr.2025.109929 · Cited by 8
Scalable and robust regression models for continuous proportional data
Lee, C. J., Dahl, B. K., Ovaskainen, O., & Dunson, D. (2025) · Journal of the American Statistical Association · doi:10.1080/01621459.2026.2626081 · Cited by 8
Shannon, E. S., Finley, A. O., May, P. B., Domke, G., Andersen, H.-E., Gaines, G. C., Nothdurft, A., & Banerjee, S. (2025) · Forest Ecology and Management · doi:10.1016/j.foreco.2025.122999 · Cited by 8
An updated landslide susceptibility model and a log-Gaussian Cox process extension for Scotland
Bryce, E., Castro‐Camilo, D., Dashwood, C., Tanyaş, H., Ciurean, R. L., Novellino, A., & Lombardo, L. (2024) · Landslides · doi:10.1007/s10346-024-02368-9 · Cited by 9
“This procedure calculates the Deviance Information Criterion and the Watanabe-Akaike Information Criterion (DIC and WAIC respectively; Meyer 2014; Gelman et al. 2014).”
Kong, S., Qin, Y.-L., Shi, X.-X., Yu, J., Jia, L.-G., Chen, Y., & Fan, M. (2024) · Frontiers in Plant Science · doi:10.3389/fpls.2024.1458741 · Cited by 8
“It considers all sources of uncertainty using the Markov algorithm and converts them into probability distributions (Gelman et al., 2014; Je ́ go et al., 2022).”
MethodInference on the Macroscopic Dynamics of Spiking Neurons
Baldy, N., Breyton, M., Woodman, M., Jirsa, V., & Hashemi, M. (2024) · Neural Computation · doi:10.1162/neco_a_01701 · Cited by 12
“…can be achieved through Bayesian model comparison by computing information criteria from a Bayesian perspective, such as the widely applicable information criterion (Watanabe, 2010) and expected log predictive density using leave-one-out cross-validation (Vehtari et al., 2016; Gelman et al., 2013).”
BackgroundZhang, X., Ryan, A., & Wu, Y.-J. (2024) · Journal of Transportation Safety & Security · doi:10.1080/19439962.2024.2325399 · Cited by 8
“The detailed LOO-CV process can be found in (Gelman et al., 2013).”
Iong, D., McAnear, M., Qu, Y., Zou, S., Toth, G., & Chen, Y. (2024) · Data Science in Science · doi:10.1080/26941899.2024.2383281 · Cited by 8
“…as The MAE between y and ˆ y is defined as The NLPD is defined as the average negative log value of the predictive distribution at test inputs X ∗ with test outputs y ∗ : This measure is commonly used to compare predictive performance on unseen data among different models (Gelman et al. 2014).”
MethodHeo, I., Jia, F., & Depaoli, S. A. (2023) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2023.2264514 · Cited by 8
“A detailed exposition is provided by Daniels and Hogan (2008) and Gelman et al. (2013) of how data augmentation works for obtaining posterior estimates— under both ignorable missingness (i.e., missing at random [MAR] and missing completely at random [MCAR]) and nonignorable missingness (i.e.,…”
BackgroundA Spike-and-Slab Prior for Dimension Selection in Generalized Linear Network Eigenmodels
Loyal, J. D., & Chen, Y.-G. (2023) · doi:10.48550/arxiv.2309.11654 · Cited by 8
“We use the definitions of the various information criteria as outlined in Gelman et al. (2014). Each criterion contains two terms, the first term measures model fit, while the second term penalizes model complexity.”
MethodMarsh, D. M., Medina, J., & Wilkinson, B. (2023) · Urban Ecosystems · doi:10.1007/s11252-023-01437-6 · Cited by 7
“To compare predictive accuracy, we used the mean of the squared deviation between the observed and expected values for richness as a scoring function (Gelman et al. 2014).”
G'omez-M'endez, I., & Amornbunchornvej, C. (2023) · Heliyon · doi:10.1016/j.heliyon.2024.e27968 · Cited by 8
A Novel Class of Unfolding Models for Binary Preference Data
Lei, R., & Rodríguez, A. (2023) · Political Analysis · doi:10.1017/pan.2024.11 · Cited by 8
“We start by comparing the fit of the various models using a blocked version of the Watanabe-Akaike Information Criterion (WAIC, Watanabe and Opper 2010; Watanabe 2013; Gelman, Hwang, and Vehtari 2014).”
MethodOn Masked Pre-training and the Marginal Likelihood
Moreno-Muñoz, P., Recasens, P. G., & Hauberg, S. (2023) · neural information processing systems · doi:10.52202/075280-3493 · Cited by 4
“Earlier works (Vehtari and Lampinen, 2002; Gelman et al., 2014) also provided a Bayesian perspective of CV .”
MethodSpatio-Temporal Stick-Breaking Process
Grazian, C. (2023) · Bayesian Analysis · doi:10.1214/24-ba1419 · Cited by 8
The Effect of Multi-Use Landscapes on Mammal Assemblages and Its Implication for Conservation
Woodgate, Z., Drouilly, M., Distiller, G. B., & O'Riain, M. J. (2023) · Land · doi:10.3390/land12030599 · Cited by 8
Bayesian hierarchical models and prior elicitation for fitting psychometric functions
Mezzetti, M., Ryan, C. P., Balestrucci, P., Lacquaniti, F., & Moscatelli, A. (2023) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2023.1108311 · Cited by 11
“To compare Bayesian models, different indicators can be adopted (Gelfand and Dey, 1994; Wasserman, 2000; Gelman et al., 2014).”
Miller, R. A., Buchanan, J., Pope, T., Carlisle, J. D., Moulton, C. E., & Booms, T. L. (2023) · Journal of Wildlife Management · doi:10.1002/jwmg.22369 · Cited by 8
Using population monitoring programs to detect changes in mammalian communities
Chaudhary, V., Goswami, V. R., Jones, G., Toh, K. B., Tapi, T., Ri, C., Kéry, M., & Oli, M. (2022) · Biological Conservation · doi:10.1016/j.biocon.2022.109778 · Cited by 8
The Importance of Livestock Demography and Infrastructure in Driving Foot and Mouth Disease Dynamics
Gilbertson, K., Brommesson, P., Minter, A., Hallman, C., Miller, R. S., Portacci, K., Sellman, S., Tildesley, M., Webb, C., Lindström, T., et al. (2022) · Life · doi:10.3390/life12101604 · Cited by 8
“[34]) the posterior sample variance of the log predictive density as penalty term.”
BackgroundMethodEllis, K. S., Pearse, A. T., Brandt, D. A., Bidwell, M. T., Harrell, W. C., Butler, M. J., & van der Burg, M. P. (2022) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2022.931260 · Cited by 12
Ning, L.-H. (2022) · Journal of Speech, Language and Hearing Research · doi:10.1044/2022_jslhr-21-00597 · Cited by 8
Point Event Cluster Detection via the Bayesian Generalized Fused Lasso
Masuda, R., & Inoue, R. (2022) · ISPRS Int. J. Geo Inf. · doi:10.3390/ijgi11030187 · Cited by 8
Predictive Fit Metrics for Item Response Models
Stenhaug, B., & Domingue, B. W. (2022) · Applied Psychological Measurement · doi:10.1177/01466216211066603 · Cited by 8
Consequences of migratory strategy on habitat selection by mule deer
Peterson, C. J., DeCesare, N. J., Hayes, T. A., Bishop, C. J., & Mitchell, M. S. (2021) · Journal of Wildlife Management · doi:10.1002/jwmg.22135 · Cited by 10
Meyer-Grant, C. G., & Klauer, K. C. (2021) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2021.102615 · Cited by 13
A Bayesian Generalized Explanatory Item Response Model to Account for Learning During the Test
Lozano, J. H., & Revuelta, J. (2021) · Psychometrika · doi:10.1007/s11336-021-09786-x · Cited by 8
“Stan is a programming software that implements the no-U-turn sampler (NUTS; Hoffman & Gelman, 2014), an extension of the Hamiltonian Monte Carlo (HMC; Duane et al., 1987; Neal, 1994, 2011) algorithm.”
MethodLi, M., Lan, L., Luo, J., Li, P., Li, X., & Zhou, X. (2021) · Frontiers in Public Health · doi:10.3389/fpubh.2021.726140 · Cited by 8
“The CVIC was defined as CVIC = −2 × log [P (X|M)], where P (X|M) is the probability of the data X for a particular subtypes-progression modelM.”
MethodInfluential
Metadata
- Authors
- Gelman, A., Hwang, J., & Vehtari, A.
- Affiliations
- Columbia University (US)
- Harvard University (US)
- Aalto University (FI)
- Corresponding author
- Gelman, Andrew
- Venue
- Statistics and Computing
- Published
- 2013-08-20
- Volume
- 24
- Issue
- 6
- Pages
- 997-1016
- ISSN
- 0960-3174 (ISSN-L)
- 1573-1375
- OpenAlex
- W2130902307
- Cited by
- 2,104
- References
- 42
- Citations by year
- 2026: 153 · 2025: 202 · 2024: 198 · 2023: 203 · 2022: 227 · 2021: 266 · 2020: 213 · 2019: 195 · 2018: 154 · 2017: 136 · 2016: 90 · 2015: 44 · 2014: 16 · 2013: 3
- FWCI
- 45.30
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Statistics and Computing (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Institute of Education Sciences
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- information criteria, Akaike information criterion, deviance information criterion, Bayesian model selection, out-of-sample prediction error, bias correction, model comparison
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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