相关论文: A Widely Applicable Bayesian Information Criterion

Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalised maxima of log-likelihoods for…

In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…

In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional…

Information criteria such as Akaike's (AIC) and Bayes' (BIC) are widely used for model selection in physics and beyond, quantifying the tradeoff between model complexity and goodness-of-fit to enforce parsimony. However, their derivation…

In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the…

Robust model-fitting to spectroscopic transitions is a requirement across many fields of science. The corrected Akaike and Bayesian information criteria (AICc and BIC) are most frequently used to select the optimal number of fitting…

A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an…

Information criteria, such as Akaike's information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well…

The information criterion AIC has been used successfully in many areas of statistical modeling, and since it is derived based on the Taylor expansion of the log-likelihood function and the asymptotic distribution of the maximum likelihood…

We derive a new Bayesian Information Criterion (BIC) by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

We consider a sparse linear regression model, when the number of available predictors, $p$, is much larger than the sample size, $n$, and the number of non-zero coefficients, $p_0$, is small. To choose the regression model in this…

Model selection is of fundamental importance to high dimensional modeling featured in many contemporary applications. Classical principles of model selection include the Kullback-Leibler divergence principle and the Bayesian principle,…

The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing…

In regular statistical models, the leave-one-out cross-validation is asymptotically equivalent to the Akaike information criterion. However, since many learning machines are singular statistical models, the asymptotic behavior of the…

We introduce a generalized information criterion that contains other well-known information criteria, such as Bayesian information Criterion (BIC) and Akaike information criterion (AIC), as special cases. Furthermore, the proposed spectral…

Model selection is a ubiquitous problem that arises in the application of many statistical and machine learning methods. In the likelihood and related settings, it is typical to use the method of information criteria (IC) to choose the most…

In this work, we propose a modified Bayesian Information Criterion (BIC) specifically designed for mixture models and hierarchical structures. This criterion incorporates the determinant of the Hessian matrix of the log-likelihood function,…

Regularized models have been applied in lots of areas, with high-dimensional data sets being popular. Because tuning parameter decides the theoretical performance and computational efficiency of the regularized models, tuning parameter…

When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…