Related papers: A Bayesian information criterion for singular mode…
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…
Finite mixture models are ubiquitous in modern statistical modeling, and a recurring practical issue is choosing the model order. In \citet[Sankhy\=a Series A, \textbf62, pp. 49--66]{keribin2000consistent}, the Bayesian information…
We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our main result shows that the BIC is strongly consistent for…
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…
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.…
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 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,…
Popular statistical software provides Bayesian information criterion (BIC) for multilevel models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to…
Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because…
A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In…
The stochastic expansion of the marginal quasi-likelihood function associated with a class of generalized linear models is shown. Based on the expansion, a quasi-Bayesian information criterion is proposed that is able to deal with…
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…
The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC however is not suitable for evaluating models with order constraints on the parameters of…
Performing model selection between Gibbs random fields is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical or numerical methods.…
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,…
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…
The Bayesian information criterion (BIC), defined as the observed data log likelihood minus a penalty term based on the sample size $N$, is a popular model selection criterion for factor analysis with complete data. This definition has also…
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…
Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…
The efficacy of family-based approaches to mixture model-based clustering and classification depends on the selection of parsimonious models. Current wisdom suggests the Bayesian information criterion (BIC) for mixture model selection.…