File Name: multimodal inference understanding aic and bic in model selection .zip
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The Akaike information criterion AIC is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Thus, AIC provides a means for model selection. AIC is founded on information theory. When a statistical model is used to represent the process that generated the data, the representation will almost never be exact; so some information will be lost by using the model to represent the process. AIC estimates the relative amount of information lost by a given model: the less information a model loses, the higher the quality of that model. In estimating the amount of information lost by a model, AIC deals with the trade-off between the goodness of fit of the model and the simplicity of the model. In other words, AIC deals with both the risk of overfitting and the risk of underfitting.
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. Can negative difference between BICs be interpreted as the posterior odds of one model over the other? How can I put this into words? Burnham and Anderson term this as the evidence ratio. This table shows how the evidence ratio changes with respect to the best model.
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Model Selection and Multimodel Inference
We briefly outline the information-theoretic I-T approaches to valid inference including a review of some simple methods for making formal inference from all the hypotheses in the model set multimodel inference. The I-T methods are easy to compute and understand and provide formal measures of the strength of evidence for both the null and alternative hypotheses, given the data. We give an example to highlight the importance of deriving alternative hypotheses and representing these as probability models. Fifteen technical issues are addressed to clarify various points that have appeared incorrectly in the recent literature. We offer several remarks regarding the future of empirical science and data analysis under an I-T framework. This is a preview of subscription content, access via your institution.
Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence BME , which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: 1 Exact and fast analytical solutions are limited by strong assumptions. Our study features a theory-based intercomparison of these techniques.
Akaike information criterion
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