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Perform a Bayesian regression of TBBMC on age, length, weight, and BMI (data in ‘osteoporosismultiple.txt’) with the classical NI priors using the following:

Perform a Bayesian regression of TBBMC on age, length, weight, and BMI (data in ‘osteoporosismultiple.txt’) with the classical NI priors using the following:  Basic Gibbs sampler and block Gibbs sampler with the regression parameters in one block and the residual variance parameter in another block.  Block Random Walk Metropolis sampler for the regression parameters. Use a normal proposal density and look for an appropriate scale parameter. Further, replace the normal proposal density by a multivariate t3-density.  Block Independent MH sampler for the regression parameters. Use as proposal density a normal distribution with mean the MLE and covariance matrix proportional to minus the inverse of the Hessian matrix at the MLE. Look for an appropriate proportionality factor.

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