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Massiel Orellana, Alicia Carriquiry, Jode Edwards, Jean-Luc Jannink Iowa State University

Bayesian Modeling of Heterogeneous Error and Genotype by Environment Interaction Variances: Model Assessment. Massiel Orellana, Alicia Carriquiry, Jode Edwards, Jean-Luc Jannink Iowa State University. Outline :. Motivation Bayesian Approach Bayesian Estimation Heterogeneous Model

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Massiel Orellana, Alicia Carriquiry, Jode Edwards, Jean-Luc Jannink Iowa State University

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  1. Bayesian Modeling of Heterogeneous Error and Genotype by Environment Interaction Variances: Model Assessment MassielOrellana, Alicia Carriquiry, Jode Edwards, Jean-Luc Jannink Iowa State University

  2. Outline: • Motivation • Bayesian Approach • Bayesian Estimation • Heterogeneous Model • Model Assessment • Methods • Results • Future Work

  3. Motivation: Oats Yield Trials Nashua Sutherland Ames Crawfordsville Lewis

  4. Motivation: Oats Yield Trials

  5. Motivation: Oats Yield Trials Nashua Sutherland Ames Crawfordsville Lewis

  6. Motivation: Oats Yield Trials Questions • Are variances heterogeneous? What factors predict heterogeneity? • Does a heterogeneous variance model produce better estimators of performance? • How do we estimate the parameters of interest in this model?

  7. Bayesian Approach 1st Step: The researcher makes a statement of knowledge prior to performing the experiment It can be based on physics, on the results of other experiments, on expert opinion, or any other source of relevant information Prior p(θ) 2nd Step: To improve this state of knowledge an experiment is designed and executed 3rd Step: Prior knowledge is updated Posterior p(θ|y)

  8. Bayesian Approach Heterogenous Model Yijk~N(mijk, ) mijk=Bjk+Gi+Ej+(GxE)ij ln( )=a+agi+aej ln( )=b+bgi+bej

  9. Marginal Error Variances

  10. Marginal G x E Variances

  11. Marginal Error Variances

  12. Marginal G x E Variances

  13. Model Assessment Is the model consistent with data? How is the data generated?

  14. Model Assessment • If the model fits, then replicated data generated under the model should look similar to observed data • Basic Technique: Draw simulated values from the posterior predictive distribution and compare the samples to the observed data.

  15. Model Assessment Example: 1 genotype, 1 environment,1 rep n=100 simulated outcomes of the Oat trial Observed value=30

  16. Model Assessment What kind of statistic do we need to use? -One that is useful for Oat breeders -Mean, variance? Not a good idea! • Range of genotype performance • is a measurement of stability • wide range vs narrow range

  17. Model Assessment How to quantify differences for all the genotypes and all the environments? pmse = Predicted Mean Square Error

  18. Model Assessment pmse

  19. Future Work • Try different statistics : • Incorporate data: 2004-2005 • Use different approaches – Classical approach

  20. Thank you!

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