Bayesian Inference in the Seemingly Unrelated Regressions Model

Griffiths, William E.

doi:10.1201/9780203911570.ch9

Cited by 17 publications

(16 citation statements)

References 29 publications

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“…A commonly used updating scheme for the overall means and the coefficients is performed by updating jointly m and b for all traits (see Smith and Kohn 2000;Griffiths 2001;Verzilli et al 2005). This scheme requires large matrix operations at each simulation iteration, resulting in prohibitive computational burden for genomewide multiple-QTL analysis.…”

Section: Markov Chain Monte Carlo Algorithmmentioning

confidence: 99%

“…However, conditional updates of g, l, and g are illustrated only for the SURd model, which can be easily adapted to the SURs and TMV models (see appendix b). Below, we describe our algorithm, with more details on steps for unknowns where the method involves explicit extension for multiple correlated traits.A commonly used updating scheme for the overall means and the coefficients is performed by updating jointly m and b for all traits (see Smith and Kohn 2000;Griffiths 2001;Verzilli et al 2005). This scheme requires large matrix operations at each simulation iteration, resulting in prohibitive computational burden for genomewide multiple-QTL analysis.…”

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confidence: 99%

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Bayesian Quantitative Trait Loci Mapping for Multiple Traits

2008

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Most quantitative trait loci (QTL) mapping experiments typically collect phenotypic data on multiple correlated complex traits. However, there is a lack of a comprehensive genomewide mapping strategy for correlated traits in the literature. We develop Bayesian multiple-QTL mapping methods for correlated continuous traits using two multivariate models: one that assumes the same genetic model for all traits, the traditional multivariate model, and the other known as the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We develop computationally efficient Markov chain Monte Carlo (MCMC) algorithms for performing joint analysis. We conduct extensive simulation studies to assess the performance of the proposed methods and to compare with the conventional single-trait model. Our methods have been implemented in the freely available package R/qtlbim (http:/ /www.qtlbim.org), which greatly facilitates the general usage of the Bayesian methodology for unraveling the genetic architecture of complex traits. C OMPLEX traits involve effects of a multitude of genes in an interacting network. Mapping quantitative trait loci (QTL) means inferring the genetic architecture (number of genes, their positions, and their effects) underlying these complex traits. The QTL mapping problem has several salient features: first, the predictor variables in the regression (the genotypes of QTL) are not observed; second, it is really a model selection problem as there are typically thousands of loci to choose from; and third, the genomic loci on the same chromosome are correlated. Much has been done in this regard, especially in the univariate case (e.g., Lander and Botstein 1989;Jiang and Zeng 1997;Broman and Speed 2002). Bayesian methods have been very successful in the QTL mapping framework (Satagopan and Yandell 1996;Yi and Xu 2002;Yi et al. 2003Yi et al. , 2005Yi et al. , 2007Yi 2004); see a recent review by Yi and Shriner (2008).Most of these methods are applicable to mapping QTL for a single trait. However, in QTL experiments typically data on more than one trait are collected and, more often than not, they are correlated. It seems natural to jointly analyze these correlated traits. There are two distinct advantages for jointly analyzing correlated traits: including information from all traits can increase the power to detect QTL and the precision of the estimated QTL effects. Biologically, it is imperative to jointly analyze correlated traits to answer questions like pleiotropy (one gene influencing more than one trait) and/or close linkage (different QTL physically close to each other influencing the traits). Testing these hypotheses is key to understanding the underlying biochemical pathways causing complex traits, which is the ultimate goal of QTL mapping.Several methods have been developed to jointly analyze multiple correlated traits. Some of them use a maximum-likelihood-based approach ( Jiang and Zeng 1995;Jackson et al. 1999; Williams et al. 1999a,b;Vieira et al. 2000...

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Section: Markov Chain Monte Carlo Algorithmmentioning

confidence: 99%

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confidence: 99%

Bayesian Quantitative Trait Loci Mapping for Multiple Traits

2008

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“…23 Similarly, the prior on the output growth implies that a 100 basis point change increases the probability by 0.04. These probability changes might seem small compared to the Taylor rule coefficients that have been used in the literature.…”

Section: Choice Of Priorsmentioning

confidence: 99%

A Bivariate Model of Fed and ECB Main Policy Rates

Scotti

2006

SSRN Journal

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This paper studies when and by how much the Fed and the ECB change their target interest rates. I develop a new nonlinear bivariate framework, which allows for elaborate dynamics and potential interdependence between the two countries, as opposed to linear feedback rules, such as a Taylor rule, and I use a novel real-time data set. A Bayesian estimation approach is particularly well suited to the small data sample. Empirical results support synchronization between the central banks and non-zero correlation between magnitude shocks, but they do not support follower behavior. Institutional factors and inflation represent relevant variables for timing decisions of both banks. Inflation rates are important factors for magnitude decisions, while output plays a major role in US magnitude decisions.JEL Classification: C11, C3, C52, E52

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“…Gallant and Golub (1984), Terrell (1995), or Barnett et al (1991). 25 For MCMC sampling in the context of the normal SUR model, we want to refer to the very useful exposition by Griffiths 2003 . Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Literature on applications of MHARA includeKoop et al (1994),O'Donnell et al (1999),Griffiths et al (2000),Griffiths (2003),Chua et al (2001),Cuesta et al (2001),Kleit and Terrell (2001) and O'Donnell and Coelli (2003.…”

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confidence: 98%