The Experts below are selected from a list of 12984 Experts worldwide ranked by ideXlab platform
J L Noguera - One of the best experts on this subject based on the ideXlab platform.
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Bayes Factor analyses of heritability for serum and muscle lipid traits in duroc pigs
Journal of Animal Science, 2010Co-Authors: J Casellas, J L Noguera, J Reixach, I Diaz, M Amills, R QuintanillaAbstract:: Concern about pork quality has increased during last decades. Given the influence of fat content and composition on sensorial, nutritional, and technological variables of pork meat, an accurate knowledge about genetic control of pig lipid metabolism is required. This study focused on providing a broad characterization for serum and meat lipid trait heritability estimates in pigs. Analyses were performed on a population of 370 Duroc barrows and measured the additive polygenic background for the serum concentrations of cholesterol, triglyceride, and low- and high-density lipoproteins at 45 and 190 d of age (at slaughter), as well as intramuscular fat, cholesterol content, and C:12 to C:22 fatty acid content in longissimus thoracis et lumborum and gluteus medius muscles at slaughter. These traits were analyzed under Bayesian univariate animal linear models, and the statistical relevance of heritability estimates was evaluated through Bayes Factor (BF); the model with polygenic additive effects was favored when BF >1. All serum lipid traits showed relevant genetic determinism, but the BF reached greater values at 190 d of age. Serum lipid traits displayed moderate modal estimates for heritability that ranged from 0.18 to 0.30. On the other hand, the genetic determinism for meat quality traits showed a heterogeneous behavior with large and less-than-1 BF. In general, longissimus thoracis et lumborum and gluteus medius muscles showed a similar pattern, with strong evidence of polygenic additive effects for intramuscular fat and palmitic, stearic, and cis-vaccenic fatty acids content, whereas oleic and muscle cholesterol content showed moderate to weak BF with moderate heritabilities. Similarly, results regarding linoleic, arachidonic, n-3, and n-6 fatty acids suggested a moderate genetic determinism, but only in gluteus medius muscle. For the remaining traits (myristic and palmitoleic fatty acids in both muscles, along with linoleic, arachidonic, n-3, and n-6 fatty acids in the longissimus thoracis et lumborum muscle), no statistical evidence for genetic control was observed in this study. As a whole, these results confirm the complexity of lipid metabolism in pigs.
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empirical Bayes Factor analyses of quantitative trait loci for gestation length in iberian meishan f2 sows
Animal, 2008Co-Authors: J Casellas, L Varona, C Ovilo, G Munoz, Oscar Ramirez, C Barragan, A Tomas, M Martinezginer, A Sanchez, J L NogueraAbstract:: The aim of this study was to investigate chromosomal regions affecting gestation length in sows. An experimental F2 cross between Iberian and Meishan pig breeds was used for this purpose and we genotyped 119 markers covering the 18 porcine autosomal chromosomes. Within this context, we have developed a new empirical Bayes Factor (BF) approach to compare between nested models, with and without the quantitative trait loci (QTL) effect, and after including the location of the QTL as an unknown parameter in the model. This empirical BF can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null QTL effects. Linkage analyses were performed in each chromosome using an animal model to account for infinitesimal genetic effects. Initially, three QTL were detected at chromosomes 6, 8 and 11 although, after correcting for multiple testing, only the additive QTL located in cM 110 of chromosome 8 remained. For this QTL, the allelic effect of substitution of the Iberian allele increased gestation length in 0.521 days, with a highest posterior density region at 95% ranged between 0.121 and 0.972 days. Although future studies are necessary to confirm if detected QTL is relevant and segregating in commercial pig populations, a hot-spot on the genetic regulation of gestation length in pigs seems to be located in chromosome 8.
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derivation of a Bayes Factor to distinguish between linked or pleiotropic quantitative trait loci
Genetics, 2004Co-Authors: L Varona, L Gomezraya, W M Rauw, Alex Clop, C Ovilo, J L NogueraAbstract:A simple procedure to calculate the Bayes Factor between linked and pleiotropic QTL models is presented. The Bayes Factor is calculated from the marginal prior and posterior densities of the locations of the QTL under a linkage and a pleiotropy model. The procedure is computed with a Gibbs sampler, and it can be easily applied to any model including the location of the QTL as a variable. The procedure was compared with a multivariate least-squares method. The proposed procedure showed better results in terms of power of detection of linkage when low information is available. As information increases, the performance of both procedures becomes similar. An example using data provided by an Iberian by Landrace pig intercross is presented. The results showed that three different QTL segregate in SSC6: a pleiotropic QTL affects myristic, palmitic, and eicosadienoic fatty acids; another pleiotropic QTL affects palmitoleic, stearic, and vaccenic fatty acids; and a third QTL affects the percentage of linoleic acid. In the example, the Bayes Factor approach was more powerful than the multivariate least-squares approach.
L Varona - One of the best experts on this subject based on the ideXlab platform.
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empirical Bayes Factor analyses of quantitative trait loci for gestation length in iberian meishan f2 sows
Animal, 2008Co-Authors: J Casellas, L Varona, C Ovilo, G Munoz, Oscar Ramirez, C Barragan, A Tomas, M Martinezginer, A Sanchez, J L NogueraAbstract:: The aim of this study was to investigate chromosomal regions affecting gestation length in sows. An experimental F2 cross between Iberian and Meishan pig breeds was used for this purpose and we genotyped 119 markers covering the 18 porcine autosomal chromosomes. Within this context, we have developed a new empirical Bayes Factor (BF) approach to compare between nested models, with and without the quantitative trait loci (QTL) effect, and after including the location of the QTL as an unknown parameter in the model. This empirical BF can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null QTL effects. Linkage analyses were performed in each chromosome using an animal model to account for infinitesimal genetic effects. Initially, three QTL were detected at chromosomes 6, 8 and 11 although, after correcting for multiple testing, only the additive QTL located in cM 110 of chromosome 8 remained. For this QTL, the allelic effect of substitution of the Iberian allele increased gestation length in 0.521 days, with a highest posterior density region at 95% ranged between 0.121 and 0.972 days. Although future studies are necessary to confirm if detected QTL is relevant and segregating in commercial pig populations, a hot-spot on the genetic regulation of gestation length in pigs seems to be located in chromosome 8.
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Bayes Factor for testing between different structures of random genetic groups a case study using weaning weight in bruna dels pirineus beef cattle
Genetics Selection Evolution, 2007Co-Authors: J Casellas, J Piedrafita, L VaronaAbstract:The implementation of genetic groups in BLUP evaluations accounts for different expectations of breeding values in base animals. Notwithstanding, many feasible structures of genetic groups exist and there are no analytical tools described to compare them easily. In this sense, the recent development of a simple and stable procedure to calculate the Bayes Factor between nested competing models allowed us to develop a new approach of that method focused on compared models with different structures of random genetic groups. The procedure is based on a reparameterization of the model in terms of intraclass correlation of genetic groups. The Bayes Factor can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null intraclass correlation. It compares two nested models, a model with a given structure of genetic groups against a model without genetic groups. The calculation of the Bayes Factor between different structures of genetic groups can be quickly and easily obtained from the Bayes Factor between the nested models. We applied this approach to a weaning weight data set of the Bruna dels Pirineus beef cattle, comparing several structures of genetic groups, and the final results showed that the preferable structure was an only group for unknown dams and different groups for unknown sires for each year of calving.
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derivation of a Bayes Factor to distinguish between linked or pleiotropic quantitative trait loci
Genetics, 2004Co-Authors: L Varona, L Gomezraya, W M Rauw, Alex Clop, C Ovilo, J L NogueraAbstract:A simple procedure to calculate the Bayes Factor between linked and pleiotropic QTL models is presented. The Bayes Factor is calculated from the marginal prior and posterior densities of the locations of the QTL under a linkage and a pleiotropy model. The procedure is computed with a Gibbs sampler, and it can be easily applied to any model including the location of the QTL as a variable. The procedure was compared with a multivariate least-squares method. The proposed procedure showed better results in terms of power of detection of linkage when low information is available. As information increases, the performance of both procedures becomes similar. An example using data provided by an Iberian by Landrace pig intercross is presented. The results showed that three different QTL segregate in SSC6: a pleiotropic QTL affects myristic, palmitic, and eicosadienoic fatty acids; another pleiotropic QTL affects palmitoleic, stearic, and vaccenic fatty acids; and a third QTL affects the percentage of linoleic acid. In the example, the Bayes Factor approach was more powerful than the multivariate least-squares approach.
Eric-jan Wagenmakers - One of the best experts on this subject based on the ideXlab platform.
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a tutorial on Bayes Factor design analysis using an informed prior
Behavior Research Methods, 2019Co-Authors: Angelika Stefan, Felix D Schonbrodt, Quentin Frederik Gronau, Eric-jan WagenmakersAbstract:: Well-designed experiments are likely to yield compelling evidence with efficient sample sizes. Bayes Factor Design Analysis (BFDA) is a recently developed methodology that allows researchers to balance the informativeness and efficiency of their experiment (Schonbrodt & Wagenmakers, Psychonomic Bulletin & Review, 25(1), 128-142 2018). With BFDA, researchers can control the rate of misleading evidence but, in addition, they can plan for a target strength of evidence. BFDA can be applied to fixed-N and sequential designs. In this tutorial paper, we provide an introduction to BFDA and analyze how the use of informed prior distributions affects the results of the BFDA. We also present a user-friendly web-based BFDA application that allows researchers to conduct BFDAs with ease. Two practical examples highlight how researchers can use a BFDA to plan for informative and efficient research designs.
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Bayes Factor design analysis planning for compelling evidence
Psychonomic Bulletin & Review, 2018Co-Authors: Felix D Schonbrodt, Eric-jan WagenmakersAbstract:A sizeable literature exists on the use of frequentist power analysis in the null-hypothesis significance testing (NHST) paradigm to facilitate the design of informative experiments. In contrast, there is almost no literature that discusses the design of experiments when Bayes Factors (BFs) are used as a measure of evidence. Here we explore Bayes Factor Design Analysis (BFDA) as a useful tool to design studies for maximum efficiency and informativeness. We elaborate on three possible BF designs, (a) a fixed-n design, (b) an open-ended Sequential Bayes Factor (SBF) design, where researchers can test after each participant and can stop data collection whenever there is strong evidence for either \(\mathcal {H}_{1}\) or \(\mathcal {H}_{0}\), and (c) a modified SBF design that defines a maximal sample size where data collection is stopped regardless of the current state of evidence. We demonstrate how the properties of each design (i.e., expected strength of evidence, expected sample size, expected probability of misleading evidence, expected probability of weak evidence) can be evaluated using Monte Carlo simulations and equip researchers with the necessary information to compute their own Bayesian design analyses.
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j b s haldane s contribution to the Bayes Factor hypothesis test
Statistical Science, 2017Co-Authors: Eric-jan WagenmakersAbstract:This article brings attention to some historical developments that gave rise to the Bayes Factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation—to assign prior mass to a general law—is due to a series of three articles by Dorothy Wrinch and Sir Harold Jeffreys (1919, 1921, 1923a). However, our historical investigation also suggests that in 1932, J. B. S. Haldane made an important contribution to the development of the Bayes Factor by proposing the use of a mixture prior comprising a point mass and a continuous probability density. Jeffreys was aware of Haldane’s work and it may have inspired him to pursue a more concrete statistical implementation for his conceptual ideas. It thus appears that Haldane may have played a much bigger role in the statistical development of the Bayes Factor than has hitherto been assumed.
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harold jeffreys s default Bayes Factor hypothesis tests explanation extension and application in psychology
Journal of Mathematical Psychology, 2016Co-Authors: Alexander Ly, Josine Verhagen, Eric-jan WagenmakersAbstract:Abstract Harold Jeffreys pioneered the development of default Bayes Factor hypothesis tests for standard statistical problems. Using Jeffreys’s Bayes Factor hypothesis tests, researchers can grade the decisiveness of the evidence that the data provide for a point null hypothesis H 0 versus a composite alternative hypothesis H 1 . Consequently, Jeffreys’s tests are of considerable theoretical and practical relevance for empirical researchers in general and for experimental psychologists in particular. To highlight this relevance and to facilitate the interpretation and use of Jeffreys’s Bayes Factor tests we focus on two common inferential scenarios: testing the nullity of a normal mean (i.e., the Bayesian equivalent of the t -test) and testing the nullity of a correlation. For both Bayes Factor tests, we explain their development, we extend them to one-sided problems, and we apply them to concrete examples from experimental psychology.
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Origin of the Bayes Factor
arXiv: Other Statistics, 2015Co-Authors: Eric-jan WagenmakersAbstract:This article details the historical developments that gave rise to the Bayes Factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to assign prior mass to a general law - is due to a series of three articles by Dorothy Wrinch and Sir Harold Jeffreys (1919, 1921, 1923). However, our historical investigation also suggests that in 1932 it was J.B.S. Haldane who derived the first Bayes Factor. Jeffreys was well aware of Haldane's work and it may have inspired him to pursue a more concrete statistical implementation for his conceptual ideas. It thus appears that Haldane may have had a much bigger role in the statistical development of the Bayes Factor than has hitherto been assumed.
Herbert Hoijtink - One of the best experts on this subject based on the ideXlab platform.
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Sample-size determination for the Bayesian t test and Welch’s test using the approximate adjusted fractional Bayes Factor
Behavior Research Methods, 2020Co-Authors: Qianrao Fu, Herbert Hoijtink, Mirjam MoerbeekAbstract:When two independent means μ _1 and μ _2 are compared, H _0 : μ _1 = μ _2, H _1 : μ _1≠ μ _2, and H _2 : μ _1 > μ _2 are the hypotheses of interest. This paper introduces the R package SSDbain , which can be used to determine the sample size needed to evaluate these hypotheses using the approximate adjusted fractional Bayes Factor (AAFBF) implemented in the R package bain . Both the Bayesian t test and the Bayesian Welch’s test are available in this R package. The sample size required will be calculated such that the probability that the Bayes Factor is larger than a threshold value is at least η if either the null or alternative hypothesis is true. Using the R package SSDbain and/or the tables provided in this paper, psychological researchers can easily determine the required sample size for their experiments.
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sample size determination for the Bayesian t test and welch s test using the approximate adjusted fractional Bayes Factor
Behavior Research Methods, 2020Co-Authors: Qianrao Fu, Herbert Hoijtink, Mirjam MoerbeekAbstract:When two independent means μ1 and μ2 are compared, H0 : μ1 = μ2, H1 : μ1≠μ2, and H2 : μ1 > μ2 are the hypotheses of interest. This paper introduces the R package SSDbain, which can be used to determine the sample size needed to evaluate these hypotheses using the approximate adjusted fractional Bayes Factor (AAFBF) implemented in the R package bain. Both the Bayesian t test and the Bayesian Welch’s test are available in this R package. The sample size required will be calculated such that the probability that the Bayes Factor is larger than a threshold value is at least η if either the null or alternative hypothesis is true. Using the R package SSDbain and/or the tables provided in this paper, psychological researchers can easily determine the required sample size for their experiments.
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bfpack flexible Bayes Factor testing of scientific theories in r
arXiv: Computation, 2019Co-Authors: Joris Mulder, Xin Gu, Janosch Menke, Herbert Hoijtink, Anton Olssoncollentine, Andrew Tomarken, Florian Boingmessing, Marlyne Meijerink, Donald R Williams, Yves RosseelAbstract:There has been a tremendous methodological development of Bayes Factors for hypothesis testing in the social and behavioral sciences, and related fields. This development is due to the flexibility of the Bayes Factor for testing multiple hypotheses simultaneously, the ability to test complex hypotheses involving equality as well as order constraints on the parameters of interest, and the interpretability of the outcome as the weight of evidence provided by the data in support of competing scientific theories. The available software tools for Bayesian hypothesis testing are still limited however. In this paper we present a new R-package called BFpack that contains functions for Bayes Factor hypothesis testing for the many common testing problems. The software includes novel tools (i) for Bayesian exploratory testing (null vs positive vs negative effects), (ii) for Bayesian confirmatory testing (competing hypotheses with equality and/or order constraints), (iii) for common statistical analyses, such as linear regression, generalized linear models, (multivariate) analysis of (co)variance, correlation analysis, and random intercept models, (iv) using default priors, and (v) while allowing data to contain missing observations that are missing at random.
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a tutorial on testing hypotheses using the Bayes Factor
Psychological Methods, 2019Co-Authors: Herbert Hoijtink, Joris Mulder, Caspar J. Van Lissa, Xin GuAbstract:: Learning about hypothesis evaluation using the Bayes Factor could enhance psychological research. In contrast to null-hypothesis significance testing it renders the evidence in favor of each of the hypotheses under consideration (it can be used to quantify support for the null-hypothesis) instead of a dichotomous reject/do-not-reject decision; it can straightforwardly be used for the evaluation of multiple hypotheses without having to bother about the proper manner to account for multiple testing; and it allows continuous reevaluation of hypotheses after additional data have been collected (Bayesian updating). This tutorial addresses researchers considering to evaluate their hypotheses by means of the Bayes Factor. The focus is completely applied and each topic discussed is illustrated using Bayes Factors for the evaluation of hypotheses in the context of an ANOVA model, obtained using the R package bain. Readers can execute all the analyses presented while reading this tutorial if they download bain and the R-codes used. It will be elaborated in a completely nontechnical manner: what the Bayes Factor is, how it can be obtained, how Bayes Factors should be interpreted, and what can be done with Bayes Factors. After reading this tutorial and executing the associated code, researchers will be able to use their own data for the evaluation of hypotheses by means of the Bayes Factor, not only in the context of ANOVA models, but also in the context of other statistical models. (PsycINFO Database Record (c) 2019 APA, all rights reserved).
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A tutorial on testing hypotheses using the Bayes Factor
2019Co-Authors: Herbert Hoijtink, Joris Mulder, Caspar J. Van Lissa, Xin GuAbstract:Learning about hypothesis evaluation using the Bayes Factor could enhance psychologicalresearch. In contrast to null-hypothesis significance testing: it renders the evidence in favorof each of the hypotheses under consideration (it can be used to quantify support for thenull-hypothesis) instead of a dichotomous reject/do-not-reject decision; it canstraightforwardly be used for the evaluation of multiple hypotheses without having tobother about the proper manner to account for multiple testing; and, it allows continuousre-evaluation of hypotheses after additional data have been collected (Bayesian updating).This tutorial addresses researchers considering to evaluate their hypotheses by meansof the Bayes Factor. The focus is completely applied and each topic discussed is illustratedusing Bayes Factors for the evaluation of hypotheses in the context of an ANOVA model,obtained using the R package bain. Readers can execute all the analyses presented whilereading this tutorial if they download bain and the R-codes used. It will be elaborated in acompletely non-technical manner: what the Bayes Factor is, how it can be obtained, howBayes Factors should be interpreted, and what can be done with Bayes Factors. Afterreading this tutorial and executing the associated code, researchers will be able to use theirown data for the evaluation of hypotheses by means of the Bayes Factor, not only in thecontext of ANOVA models, but also in the context of other statistical models.
Min Wang - One of the best experts on this subject based on the ideXlab platform.
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consistency of Bayes Factor for nonnested model selection when the model dimension grows
Bernoulli, 2016Co-Authors: Min Wang, Yuzo MaruyamaAbstract:Zellner's $g$-prior is a popular prior choice for the model selection problems in the context of normal regression models. Wang and Sun [J. Statist. Plann. Inference 147 (2014) 95-105] recently adopt this prior and put a special hyper-prior for $g$, which results in a closed-form expression of Bayes Factor for nested linear model comparisons. They have shown that under very general conditions, the Bayes Factor is consistent when two competing models are of order $O(n^{\tau})$ for $\tau <1$ and for $\tau=1$ is almost consistent except a small inconsistency region around the null hypothesis. In this paper, we study Bayes Factor consistency for nonnested linear models with a growing number of parameters. Some of the proposed results generalize the ones of the Bayes Factor for the case of nested linear models. Specifically, we compare the asymptotic behaviors between the proposed Bayes Factor and the intrinsic Bayes Factor in the literature.
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Consistency of Bayes Factor for nonnested model selection when the model dimension grows
Bernoulli, 2016Co-Authors: Min Wang, Yuzo MaruyamaAbstract:Zellner's $g$-prior is a popular prior choice for the model selection problems in the context of normal regression models. Wang and Sun [J. Statist. Plann. Inference 147 (2014) 95-105] recently adopt this prior and put a special hyper-prior for $g$, which results in a closed-form expression of Bayes Factor for nested linear model comparisons. They have shown that under very general conditions, the Bayes Factor is consistent when two competing models are of order $O(n^{\tau})$ for $\tau
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on the consistency of the objective Bayes Factor for the integral priors in the one way random effects model
Statistics & Probability Letters, 2015Co-Authors: Shuaimin Kang, Min Wang, Tao LuAbstract:The Bayes Factor for the integral priors in the one-way random effects model has recently been developed by Cano et al. (2007). We establish the consistency of this Bayes Factor when the number of groups goes to infinity, when the number of observations per group goes to infinity, and when both go to infinity.
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Bayes Factor consistency for nested linear models with a growing number of parameters
Journal of Statistical Planning and Inference, 2014Co-Authors: Min WangAbstract:Abstract In this paper, we consider the Bayesian approach to the model selection problem for nested linear regression models. Common Bayesian procedures to this problem are based on Zellner's g-prior with a hyper-prior for the scaling Factor g. Maruyama and George (2011) recently adopted this procedure with the beta-prime distribution for g and derived an explicit closed-form Bayes Factor without integral representation which is thus easy to compute. In addition, they have studied its corresponding model selection consistency for fixed number of parameters. Over recent years, linear regression models with a growing number of unknown parameters have gained increased popularity in practical applications, such as the clustering problem. This observation motivates us to further investigate the consistency of Bayes Factor with the beta-prime distribution for g under a scenario in which the number of parameters increases with the sample size. Finally, the results presented here are compared with the ones for the Bayes Factor under intrinsic priors in relevant literature.
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Bayes Factor consistency for unbalanced anova models
Statistics, 2013Co-Authors: Min WangAbstract:In practical situations, most experimental designs often yield unbalanced data which have different numbers of observations per unit because of cost constraints, missing data, etc. In this paper, we consider the Bayesian approach to hypothesis testing or model selection under the one-way unbalanced fixed-effects analysis-of-variance (ANOVA) model. We adopt Zellner's g-prior with the beta-prime distribution for g, which results in an explicit closed-form expression of the Bayes Factor without integral representation. Furthermore, we investigate the model selection consistency of the Bayes Factor under three different asymptotic scenarios: either the number of units goes to infinity, the number of observations per unit goes to infinity, or both go to infinity. The results presented extend some existing ones of the Bayes Factor for the balanced ANOVA models in the literature.
