Bayes factors for detection of Quantitative Trait Loci

Abstract

-A fundamental issue in quantitative trait locus (QTL) mapping is to determine the plausibility of the presence of a QTL at a given genome location. Bayesian analysis offers an attractive way of testing alternative models (here, QTL vs. no-QTL) via the Bayes factor. There have been several numerical approaches to computing the Bayes factor, mostly based on Markov Chain Monte Carlo (MCMC), but these strategies are subject to numerical or stability problems. We propose a simple and stable approach to calculating the Bayes factor between nested models. The procedure is based on a reparameterization of a variance component model in terms of intra-class correlation. The Bayes factor can then be easily calculated from the output of a MCMC scheme by averaging conditional densities at the null intra-class correlation. We studied the performance of the method using simulation. We applied this approach to QTL analysis in an outbred population. We also compared it with the Likelihood Ratio Test and we analyzed its stability. Simulation results were very similar to the simulated parameters. The posterior probability of the QTL model increases as the QTL effect does. The location of the QTL was also correctly obtained. The use of meta-analysis is suggested from the properties of the Bayes factor. Bayes factor / Quantitative Trait Loci / hypothesis testing / Markov Chain Monte Carlo

Variability-specific differential gene expression across reproductive stages in sows

“…On the other hand, within-probe homogeneous residual variances are corroborated under BF HE=HO i o 1. Following Casellas, Martínez-Giner, Pena, Balcells, Ferná ndez-Rodríguez, Ibá ñ ez-Escriche and Noguera García-Corté s et al (2001) and Varona et al (2001), the posterior density p(p i 5 0.5jy) suffices to obtain BF HE=HO i ,…”

“…Note that this prior distribution is the key point for further testing of within-probe heteroskedasticity and covers all possible values taken for p k with equal probability, following Verdinelli and Wasserman (1995), García-Corté s et al (2001) and Varona et al (2001).…”

Bayes factor between Student t and Gaussian mixed models within an animal breeding context

“…The Bayes factor developed by Verdinelli and Wasserman [25], and applied to the animal breeding context by García-Cortés et al [5] and Varona et al [23], contrasts nested linear models that only differ in terms of a bounded variable. We adapted this methodology to compare a Student t mixed linear model with its simplification to the Gaussian mixed linear model when m tends to infinity or, for mathematical convenience, d = 2/m = 0.…”

“…However, they imply high computational demands because both the Gaussian and the Student t mixed model must be analysed to calculate the corresponding comparison parameter. Within this context, the Bayes factor developed by García-Cortés et al [5] and Varona et al [23] in the animal breeding context implies a substantial simplification because it compares two models that only differ in terms of a single bounded variable, and therefore only the analysis of the complex model is required. The Student t distribution converges with the Gaussian distribution when the number of degrees of freedom tends to infinity.…”

“…The Student t distribution converges with the Gaussian distribution when the number of degrees of freedom tends to infinity. This property can be exploited 396 to appropriately adapt Varona et al [23] Bayes factor, generating a useful statistical tool for the analysis of field data, especially when used for genetic evaluation purposes. In this paper, we focused our efforts on describing the development of this Bayes factor to make comparisons between Gaussian and Student t processes, and we tested its performance on both simulated and real data sets, using DIC as the standard reference criterion.…”