Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs

Cs, Wang; Rutledge, JJ; Gianola, Daniel

doi:10.1186/1297-9686-26-2-91

Cited by 192 publications

(106 citation statements)

References 1 publication

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“…adopted a proper bounded uniform prior on β, which is equivalent to specifying V −1 ββ = 0 p×p but with values of β constrained to be within the specified bounds. Then, it can be readily shown using results from Wang et al [18] that the FCD of θ is multivariate normal, that is,…”

Section: Discussionmentioning

confidence: 99%

“…(A.5) That is, a random draw from (A.5) is equivalent to a random draw from (A.1) followed by a random draw from p γ t , δ t |a p , m p , G, s * = s (k) that can be readily derived as a sequence of univariate draws from the additive γ (k) j and maternal δ (k) j Mendelian sampling terms. Specifically, this involves sampling first from (1) Draw samples of β, a p , and m p from (A.1) using the proposition from the appendix of Wang et al [18]. (2) Draw samples of γ t and δ t from (A.6) and (A.7).…”

Section: Discussionmentioning

confidence: 99%

“…Their sire model implementation combines data and prior information to determine the posterior probabilities of sire assignments for each animal with uncertain paternity. With the advent of Markov chain Monte Carlo (MCMC) techniques in animal breeding [18], it is now possible to extend their method to an animal model and allow a more formal assessment of statistical uncertainty on genetic merit and of probabilities of sire assignments.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian inference on genetic merit under uncertain paternity

Cardoso

Tempelman

2003

Genet. Sel. Evol.

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-A hierarchical animal model was developed for inference on genetic merit of livestock with uncertain paternity. Fully conditional posterior distributions for fixed and genetic effects, variance components, sire assignments and their probabilities are derived to facilitate a Bayesian inference strategy using MCMC methods. We compared this model to a model based on the Henderson average numerator relationship (ANRM) in a simulation study with 10 replicated datasets generated for each of two traits. Trait 1 had a medium heritability (h 2 ) for each of direct and maternal genetic effects whereas Trait 2 had a high h 2 attributable only to direct effects. The average posterior probabilities inferred on the true sire were between 1 and 10% larger than the corresponding priors (the inverse of the number of candidate sires in a mating pasture) for Trait 1 and between 4 and 13% larger than the corresponding priors for Trait 2. The predicted additive and maternal genetic effects were very similar using both models; however, model choice criteria (Pseudo Bayes Factor and Deviance Information Criterion) decisively favored the proposed hierarchical model over the ANRM model. uncertain paternity / multiple-sire / genetic merit / Bayesian inference / reduced animal model

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian inference on genetic merit under uncertain paternity

Cardoso

Tempelman

2003

Genet. Sel. Evol.

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“…This BF tests probe-by-probe dispersion patterns, although it does not inform about the best analytical model for the joint inference of all probes . The BF between Model HE and Model HO i (BF HE=HO i ) was calculated from the Markov chain Monte Carlo sampler output of Model HE, by averaging the full conditional densities of each cycle at p i 5 0.5 using the Rao-Blackwell argument (Wang et al, 1994). Note that BF HE=HO i 4 1 shows that Model HE is more suitable than Model HO i , revealing a statistically relevant degree of heteroskedasticity in probe i.…”

Section: Methodsmentioning

confidence: 99%

Variability-specific differential gene expression across reproductive stages in sows

Casellas

Martínez-Giner²,

Pena³

et al. 2013

Animal

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Differential gene expression analyses typically focus on departures across mathematical expectations (i.e. mean) from two or more groups of microarrays, without considering alternative patterns of departure. Nevertheless, recent studies in humans and great apes have suggested that differential gene expression could also be characterized in terms of heterogeneous dispersion patterns. This must be viewed as a very interesting genetic phenomenon clearly linked to the regulation mechanisms of gene transcription. Unfortunately, we completely lack information about the incidence and relevance of dispersion-specific differential gene expression in livestock species, although a specific Bayes factor (BF) for testing this kind of differential gene expression (i.e. within-probe heteroskedasticity) has been recently developed. Within this context, our main objective was to characterize the incidence of dispersion-specific differential gene expression in pigs and, if possible, providing the first evidence of this phenomenon in a livestock species. We evaluated dispersion-specific differential gene expression on ovary, uterus and hypophysis samples from 22 F2 Iberian × Meishan sows, where a total of 15 252 probes were interrogated. For each tissue, heteroskedasticity of probe-specific residual variances was evaluated by three pairwise comparisons involving three physiological stages, that is, heat, 15 days of pregnancy and 45 days of pregnancy. Between 2.9% and 37.4% of the analyzed probes provided statistical evidence of within-tissue across-physiological stages dispersion-specific differential gene expression (BF >1), and between 0.1% and 3.0% of them reported decisive evidence (BF >100). It is important to highlight that <8% of the heteroskedastic probes were also linked to differential gene expression in terms of departures among the probe-specific mathematical expectation of each physiological stage. This discarded the disturbance of scale effects in a high percentage of probes and suggested that probe-specific heteroskedasticity must be viewed as an independent phenomenon within the context of differential gene expression. As a whole, our results report a remarkable incidence of dispersion-specific differential gene expression across the whole genome of the pig, establishing a very interesting starting point for further studies focused on deciphering the genetic mechanisms underlying heteroskedasticity.

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“…In many studies flat priors have been used for the genetic (co)variance matrix in order to account for the lack of prior knowledge or the reluctance to use existing prior knowledge e.g. [28]. For linear models it has been shown that flat priors may lead to proper posteriors, but that they do not necessarily [5,7].…”

Section: Introductionmentioning

confidence: 99%

Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling

2007

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-Simulated data were used to investigate the influence of the choice of priors on estimation of genetic parameters in multivariate threshold models using Gibbs sampling. We simulated additive values, residuals and fixed effects for one continuous trait and liabilities of four binary traits, and QTL effects for one of the liabilities. Within each of four replicates six different datasets were generated which resembled different practical scenarios in horses with respect to number and distribution of animals with trait records and availability of QTL information. (Co)Variance components were estimated using a Bayesian threshold animal model via Gibbs sampling. The Gibbs sampler was implemented with both a flat and a proper prior for the genetic covariance matrix. Convergence problems were encountered in > 50% of flat prior analyses, with indications of potential or near posterior impropriety between about round 10 000 and 100 000. Terminations due to non-positive definite genetic covariance matrix occurred in flat prior analyses of the smallest datasets. Use of a proper prior resulted in improved mixing and convergence of the Gibbs chain. In order to avoid (near) impropriety of posteriors and extremely poorly mixing Gibbs chains, a proper prior should be used for the genetic covariance matrix when implementing the Gibbs sampler.Gibbs sampling / multivariate threshold model / covariance estimates / flat prior / proper prior

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Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs

Cited by 192 publications

References 1 publication

Bayesian inference on genetic merit under uncertain paternity

Bayesian inference on genetic merit under uncertain paternity

Variability-specific differential gene expression across reproductive stages in sows

Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling

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