Version Of Bayesian Information Criterion Research Articles

The effective sample size in Bayesian information criterion for level-specific fixed and random-effect selection in a two-level nested model.

Popular statistical software provides the Bayesian information criterion (BIC) for multi-level models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to discrepancies in the formulas of the BIC and uncertainties as to the proper use of the BIC in selecting a multi-level model with respect to level-specific fixed and random effects. These discrepancies and uncertainties result from different specifications of sample size in the BIC's penalty term for multi-level models. In this study, we derive the BIC's penalty term for level-specific fixed- and random-effect selection in a two-level nested design. In this new version of BIC, called , this penalty term is decomposed into two parts if the random-effect variance-covariance matrix has full rank: (a) a term with the log of average sample size per cluster and (b) the total number of parameters times the log of the total number of clusters. Furthermore, we derive the new version of BIC, called , in the presence of redundant random effects. We show that the derived formulae, and , adhere to empirical values via numerical demonstration and that ( indicating either or ) is the best global selection criterion, as it performs at least as well as BIC with the total sample size and BIC with the number of clusters across various multi-level conditions through a simulation study. In addition, the use of is illustrated with a textbook example dataset.

Adaptive modelling of gene regulatory network using Bayesian information criterion-guided sparse regression approach.

Inferring gene regulatory networks (GRNs) from microarray expression data are an important but challenging issue in systems biology. In this study, the authors propose a Bayesian information criterion (BIC)-guided sparse regression approach for GRN reconstruction. This approach can adaptively model GRNs by optimising the l1-norm regularisation of sparse regression based on a modified version of BIC. The use of the regularisation strategy ensures the inferred GRNs to be as sparse as natural, while the modified BIC allows incorporating prior knowledge on expression regulation and thus avoids the overestimation of expression regulators as usual. Especially, the proposed method provides a clear interpretation of combinatorial regulations of gene expression by optimally extracting regulation coordination for a given target gene. Experimental results on both simulation data and real-world microarray data demonstrate the competent performance of discovering regulatory relationships in GRN reconstruction.

Semiparametric Bayesian information criterion for model selection in ultra-high dimensional additive models

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 justification that the effects of the covariates are actually linear. Thus a semiparametric model, such as the additive model studied here, is a viable alternative. We demonstrate that theoretical results on the consistency of the BIC-type criterion can be extended to this more challenging situation, with dimension diverging exponentially fast with sample size. Besides, the assumptions on the distribution of the noises are relaxed in our theoretical studies. These efforts significantly enlarge the applicability of the criterion to a more general class of models.

Modified versions of Bayesian Information Criterion for genome-wide association studies

For the vast majority of genome-wide association studies (GWAS) statistical analysis was performed by testing markers individually. Elementary statistical considerations clearly show that in the case of complex traits an approach based on multiple regression or generalized linear models is preferable to testing single markers. A model selection approach to GWAS can be based on modifications of the Bayesian Information Criterion (BIC), where some search strategies are necessary to deal with a huge number of potential models. Comprehensive simulations based on real SNP data confirm that model selection has larger power to detect causal SNPs in complex models than single-marker tests. Furthermore, testing single markers leads to substantial problems with proper ranking of causal SNPs and tends to detect a certain number of false positive SNPs, which are not linked to any of the causal mutations. This behavior of single-marker tests is typical in GWAS for complex traits and can be explained by an aggregated influence of many small random sample correlations between genotypes of the SNP under investigation and other causal SNPs. These findings might at least partially explain problems with low power and nonreplicability of results in GWAS. A real data analysis illustrates advantages of model selection in practice, where publicly available gene expression data as traits for individuals from the HapMap project are reanalyzed.

Extending the Modified Bayesian Information Criterion (mBIC) to Dense Markers and Multiple Interval Mapping

The modified version of Bayesian Information Criterion (mBIC) is a relatively simple model selection procedure that can be used when locating multiple interacting quantitative trait loci (QTL). Our earlier work demonstrated the statistical properties of mBIC for situations where the average genetic map interval is at least 5 cM. In this work mBIC is adapted to genome searches based on a dense map and, more importantly, to the situation where consecutive QTL and interactions are located by multiple interval mapping. Easy to use formulas for the extended mBIC are given. A simulation study, as well as the analysis of real data, confirm the good properties of the extended mBIC.

Statistical Modeling of Candidate Gene Effects on Milk Production Traits in Dairy Cattle

A major objective of dairy cattle genomic research is to identify genes underlying the variability of milk production traits that could be useful in breeding programs. The candidate gene approach provides tools for searching for causative polymorphisms affecting quantitative traits. Genes with a possible effect on milk traits in cattle can be involved in different physiological pathways, such as triglyceride synthesis [acyl-CoA:diacylglycerol acyltransferase 1 gene (DGAT1)], fat secretion from the mammary epithelial tissue (butyrophilin), or entire-body energy homeostasis regulation (leptin and leptin receptor). In this study, based on data from 252 Black and White bulls from the active Polish dairy population, effects and potential interactions of 9 single nucleotide polymorphisms in the butyrophilin, DGAT1, leptin, and leptin receptor genes were investigated. Additionally, the effect of the number of additive, dominance, and epistatic genetic effects fitted into the model on the estimates of model parameters and model selection was illustrated. Phenotypic records were daughter yield deviations for milk, fat, and protein yields, obtained from a routine national genetic evaluation. Out of all the analyzed polymorphisms, DGAT1 K232A had a much larger effect on milk traits than the other single nucleotide polymorphisms considered. Estimates of the additive genetic effect of K232A expressed as half of the difference between Lys- and Ala-encoding variants were −107.4kg of milk, 5.4kg of fat, and −1.6kg of protein at first parity, as well as −120kg of milk and 6.8kg of fat at second parity. In terms of model selection, it was demonstrated that the modified version of Bayesian information criterion selects models with the parameterization reflecting the genetic background of the analyzed trait, while the Bayesian information criterion chooses models that are too highly parameterized.