Strictly Proper Scoring Rules, Prediction, and Estimation

Gneiting, Tilmann; Raftery, Adrian E.

doi:10.1198/016214506000001437

Cited by 4,191 publications

(3,429 citation statements)

References 8 publications

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“…Indeed, proper scoring rules are a fundamental concept of Bayesian inference (Bernardo and Smith, 2000). The use of a strictly proper score function guarantees that optimal predictions are elicited (Savage, 1971;Matheson and Winkler, 1976;Gneiting and Raftery, 2007). In this article we have exclusively considered to evaluate directly the predicted risk and not used risk classes.…”

Section: Summary and Discussionmentioning

confidence: 99%

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The Performance of Risk Prediction Models

Gerds¹,

Cai²,

2008

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SummaryFor medical decision making and patient information, predictions of future status variables play an important role. Risk prediction models can be derived with many different statistical approaches. To compare them, measures of predictive performance are derived from ROC methodology and from probability forecasting theory. These tools can be applied to assess single markers, multivariable regression models and complex model selection algorithms. This article provides a systematic review of the modern way of assessing risk prediction models. Particular attention is put on proper benchmarks and resampling techniques that are important for the interpretation of measured performance. All methods are illustrated with data from a clinical study in head and neck cancer patients.

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Section: Summary and Discussionmentioning

confidence: 99%

“…A scoring rule is called proper (strictly proper) if it is minimized (uniquely) at the true status probability Fðt j X i Þ (Savage, 1971;Gneiting and Raftery, 2007). An often considered strictly proper scoring rule is the Brier score (Brier, 1950).…”

Section: Expected Lossmentioning

confidence: 99%

The Performance of Risk Prediction Models

Gerds¹,

Cai²,

2008

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“…where F is the predictive cumulative distribution and y is the observed value (Matheson and Winkler, 1976;Unger, 1985;Gneiting and Raftery, 2007). While RMSE only assesses the posterior predictive mean, the whole posterior predictive distribution is taken into consideration with CRPS.…”

Section: Model Assessmentmentioning

confidence: 99%

Spatial models with explanatory variables in the dependence structure

2014

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Please cite this article as: Ingebrigtsen, R., Lindgren, F., Steinsland, I., Spatial models with explanatory variables in the dependence structure. Spatial Statistics (2013), http://dx.doi.org/10. 1016/j.spasta.2013.06.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractGeostatistical models have traditionally been stationary. However, physical knowledge about underlying spatial processes often require models with nonstationary dependence structures. Thus, there has been an interest in the literature to provide flexible models and computationally efficient methods for non-stationary phenomena. In this work, we demonstrate that the stochastic partial differential equation (SPDE) approach to spatial modelling provides a flexible class of non-stationary models where explanatory variables easily can be included in the dependence structure. In addition, the SPDE approach enables computationally efficient Bayesian inference with integrated nested Laplace approximations (INLA) available through the R-package r-inla. We illustrate the suggested modelling framework with a case study of annual precipitation in southern Norway, and compare a non-stationary model with dependence structure governed by elevation to a stationary model. Further, we use a simulation study to explore the annual precipitation models. We investigate identifiability of model parameters and whether the deviance information criterion (DIC) is able to distinguish datasets from the non-stationary and stationary models.

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“…The mean logarithmic CPO can be identified as the cross-validated logarithmic score (Gneiting and Raftery, 2007), which measures the predictive quality of a model. Lower values of the mean logarithmic CPO indicate a better model.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Sensitivity analysis in Bayesian nonignorable selection model for binary responses

Choi¹,

Kim²

2014

Journal of the Korean Data and Information Science Society

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We consider a Bayesian nonignorable selection model to accommodate the selection bias. Markov chain Monte Carlo methods is known to be very useful to fit the nonignorable selection model. However, sensitivity to prior assumptions on parameters for selection mechanism is a potential problem. To quantify the sensitivity to prior assumption, the deviance information criterion and the conditional predictive ordinate are used to compare the goodness-of-fit under two different prior specifications. It turns out that the 'MLE' prior gives better fit than the 'uniform' prior in viewpoints of goodness-of-fit measures.

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Strictly Proper Scoring Rules, Prediction, and Estimation

Cited by 4,191 publications

References 8 publications

The Performance of Risk Prediction Models

The Performance of Risk Prediction Models

Spatial models with explanatory variables in the dependence structure

Sensitivity analysis in Bayesian nonignorable selection model for binary responses

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