scholarly journals A Bayesian Approach to Detect Quantitative Trait Loci Using Markov Chain Monte Carlo

Genetics ◽  
1996 ◽  
Vol 144 (2) ◽  
pp. 805-816 ◽  
Author(s):  
Jaya M Satagopan ◽  
Brian S Yandell ◽  
Michael A Newton ◽  
Thomas C Osborn
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Quantitative Trait Loci ◽  
Bayesian Approach ◽  
Quantitative Trait ◽  
Confidence Regions ◽  
Phenotypic Trait ◽  
Parameter Estimates ◽  
Trait Loci

Abstract Markov chain Monte Carlo (MCMC) techniques are applied to simultaneously identify multiple quantitative trait loci (QTL) and the magnitude of their effects. Using a Bayesian approach a multi-locus model is fit to quantitative trait and molecular marker data, instead of fitting one locus at a time. The phenotypic trait is modeled as a linear function of the additive and dominance effects of the unknown QTL genotypes. Inference summaries for the locations of the QTL and their effects are derived from the corresponding marginal posterior densities obtained by integrating the likelihood, rather than by optimizing the joint likelihood surface. This is done using MCMC by treating the unknown QTL genotypes, and any missing marker genotypes, as augmented data and then by including these unknowns in the Markov chain cycle along with the unknown parameters. Parameter estimates are obtained as means of the corresponding marginal posterior densities. High posterior density regions of the marginal densities are obtained as confidence regions. We examine flowering time data from double haploid progeny of Brassica napus to illustrate the proposed method.

scholarly journals Mapping-Linked Quantitative Trait Loci Using Bayesian Analysis and Markov Chain Monte Carlo Algorithms

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 735-743 ◽  
Author(s):  
Pekka Uimari ◽  
Ina Hoeschele
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Allele Frequencies ◽  
Mcmc Methods ◽  
Substitution Effects ◽  
Indicator Variable ◽  
Trait Loci

A Bayesian method for mapping linked quantitative trait loci (QTL) using multiple linked genetic markers is presented. Parameter estimation and hypothesis testing was implemented via Markov chain Monte Carlo (MCMC) algorithms. Parameters included were allele frequencies and substitution effects for two biallelic QTL, map positions of the QTL and markers, allele frequencies of the markers, and polygenic and residual variances. Missing data were polygenic effects and multi-locus marker-QTL genotypes. Three different MCMC schemes for testing the presence of a single or two linked QTL on the chromosome were compared. The first approach includes a model indicator variable representing two unlinked QTL affecting the trait, one linked and one unlinked QTL, or both QTL linked with the markers. The second approach incorporates an indicator variable for each QTL into the model for phenotype, allowing or not allowing for a substitution effect of a QTL on phenotype, and the third approach is based on model determination by reversible jump MCMC. Methods were evaluated empirically by analyzing simulated granddaughter designs. All methods identified correctly a second, linked QTL and did not reject the one-QTL model when there was only a single QTL and no additional or an unlinked QTL.

Study on mapping Quantitative Trait Loci for animal complex binary traits using Bayesian-Markov chain Monte Carlo approach

2006 ◽  
Vol 49 (6) ◽  
pp. 552-559 ◽  
Author(s):  
Jianfeng Liu ◽  
Yuan Zhang ◽  
Qin Zhang ◽  
Lixian Wang ◽  
Jigang Zhang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Monte Carlo Approach ◽  
Binary Traits ◽  
Trait Loci

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

scholarly journals Bayesian estimation of parameters in a regional hydrological model

2002 ◽  
Vol 6 (5) ◽  
pp. 883-898 ◽  
Author(s):  
K. Engeland ◽  
L. Gottschalk
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Hydrological Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Daily Streamflow ◽  
Likelihood Model ◽  
Simulation Errors

Abstract. This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1) process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

Bayesian Approach to Study of Unfolded Bifurcation Structure via Markov Chain Monte Carlo Method

2017 ◽  
Vol 14 (3) ◽  
pp. 1661-1666
Author(s):  
EssamO. Abdel-Rahman ◽  
Mahmoud Elmezain ◽  
Zohair.S.A. Malki ◽  
GamalA. Abd-Elmougod
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Bayesian Approach ◽  
Bifurcation Structure
Sign in / Sign up

Export Citation Format

Share Document