相关论文: Akaike's Bayesian information criterion (ABIC) or …

The Akaike information criterion (AIC) is a common tool for model selection. It is frequently used in violation of regularity conditions at parameter space singularities and boundaries. The expected AIC is generally not asymptotically…

Transient recurring phenomena are ubiquitous in many scientific fields like neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models (VAR) may be used to characterize peri-event system dynamics associated with such…

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.…

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…

Akaike's information criterion (AIC) is a measure of the quality of a statistical model for a given set of data. We can determine the best statistical model for a particular data set by the minimization of the AIC. Since we need to evaluate…

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike…

Occupancy models are typically used to determine the probability of a species being present at a given site while accounting for imperfect detection. The survey data underlying these models often include information on several predictors…

Given a random sample from a multivariate population, estimating the number of large eigenvalues of the population covariance matrix is an important problem in Statistics with wide applications in many areas. In the context of Principal…

In multivariate extreme value analysis, the estimation of the dependence structure in extremes is demanding, especially in the context of high-dimensional data. Therefore, a common approach is to reduce the model dimension by considering…

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…

We review the Akaike, deviance, and Watanabe-Akaike information criteria from a Bayesian perspective, where the goal is to estimate expected out-of-sample-prediction error using a biascorrected adjustment of within-sample error. We focus on…

Double-descent refers to the unexpected drop in test loss of a learning algorithm beyond an interpolating threshold with over-parameterization, which is not predicted by information criteria in their classical forms due to the limitations…

In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…

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…

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,…

The widely applicable Bayesian information criterion (WBIC) is a simple and fast approximation to the model evidence that has received little practical consideration. WBIC uses the fact that the log evidence can be written as an…

Geoscientists often solve inverse problems to estimate values of parameters of interest given relevant data sets. Bayesian inference solves these problems by combining probability distributions that describe uncertainties in both…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

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…

The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…