# Bayes Factor

The Experts below are selected from a list of 12984 Experts worldwide ranked by ideXlab platform

### J L Noguera – 1st expert on this subject based on the ideXlab platform

• ##### BayesFactor analyses of heritability for serum and muscle lipid traits in duroc pigs
Journal of Animal Science, 2010
Co-Authors: J Casellas, J L Noguera, J Reixach, I Diaz, M Amills, R Quintanilla

Abstract:

: 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.

• ##### empirical BayesFactor analyses of quantitative trait loci for gestation length in iberian meishan f2 sows
Animal, 2008
Co-Authors: J Casellas, L Varona, C Ovilo, G Munoz, Oscar Ramirez, C Barragan, A Tomas, M Martinezginer, A Sanchez, J L Noguera

Abstract:

: 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.

• ##### derivation of a BayesFactor to distinguish between linked or pleiotropic quantitative trait loci
Genetics, 2004
Co-Authors: L Varona, L Gomezraya, W M Rauw, Alex Clop, C Ovilo, J L Noguera

Abstract:

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 – 2nd expert on this subject based on the ideXlab platform

• ##### empirical BayesFactor analyses of quantitative trait loci for gestation length in iberian meishan f2 sows
Animal, 2008
Co-Authors: J Casellas, L Varona, C Ovilo, G Munoz, Oscar Ramirez, C Barragan, A Tomas, M Martinezginer, A Sanchez, J L Noguera

Abstract:

: 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.

• ##### BayesFactor for testing between different structures of random genetic groups a case study using weaning weight in bruna dels pirineus beef cattle
Genetics Selection Evolution, 2007
Co-Authors: J Casellas, J Piedrafita, L Varona

Abstract:

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.

• ##### derivation of a BayesFactor to distinguish between linked or pleiotropic quantitative trait loci
Genetics, 2004
Co-Authors: L Varona, L Gomezraya, W M Rauw, Alex Clop, C Ovilo, J L Noguera

Abstract:

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 – 3rd expert on this subject based on the ideXlab platform

• ##### a tutorial on BayesFactor design analysis using an informed prior
Behavior Research Methods, 2019
Co-Authors: Angelika Stefan, Felix D Schonbrodt, Quentin Frederik Gronau, Eric-jan Wagenmakers

Abstract:

: 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.

• ##### BayesFactor design analysis planning for compelling evidence
Psychonomic Bulletin & Review, 2018
Co-Authors: Felix D Schonbrodt, Eric-jan Wagenmakers

Abstract:

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.

• ##### j b s haldane s contribution to the BayesFactor hypothesis test
Statistical Science, 2017
Co-Authors: Eric-jan Wagenmakers

Abstract:

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.