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Area of Science:

  • Statistics
  • Genetics
  • Computational Biology

Background:

  • Least Absolute Shrinkage and Selection Operator (Lasso) estimation is equivalent to Bayesian posterior mode estimation.
  • Bayesian hierarchical models require hyper prior distributions for variance parameters.
  • Estimating variance parameters is crucial for accurate regression coefficient estimation.

Purpose of the Study:

  • To develop an expectation-maximization (EM) algorithm for estimating variance parameters in Bayesian hierarchical models.
  • To evaluate the performance of the EM algorithm using simulation and real data.
  • To apply the EM algorithm to regression models and quantitative trait loci (QTL) mapping.

Main Methods:

  • Developed an expectation-maximization (EM) algorithm to estimate the variance parameter of the prior distribution for regression coefficients.
  • Utilized Jeffreys' hyper prior for the variance component.
  • Applied the algorithm to standard regression, linear models with classification variables, and QTL mapping.

Main Results:

  • The EM algorithm effectively estimates variance parameters for regression coefficients.
  • Jeffreys' hyper prior generally yields desired model sparseness.
  • The algorithm successfully handles various linear models, including those with classification variables.
  • The EM algorithm can estimate genotypic values and QTL effects in QTL mapping.

Conclusions:

  • The developed EM algorithm provides an effective method for Bayesian hierarchical modeling and regression analysis.
  • The algorithm offers a robust approach for estimating model parameters and achieving variable selection.
  • This method has significant implications for genetic analysis, particularly in QTL mapping.