BMTRY 719: Bayesian Biostatistics

Contact information

Course information

Assignments

1. HW 1 (As a student noted, the conclusion in problem 1 appears to be backward!) (soln 1)
2. HW 2 (soln 2; R code)
3. HW 3
   
   • In problem 1, choose a and b of interest
   • Caution: Obtaining the exact marginal posterior distributions in parts (c) and (d) with the prior given is difficult (requires numerical integration). Please change the prior distribution to the conjugate normal-gamma form (Ibrahim, Example 5 (iii) page 21) so that these marginal posterior distributions are easily obtained exactly, unless you have already solved the problem with the given prior. Thus, take m given t to be normal with mean m₀ and precision tt₀ and t to be gamma with shape a and rate b. Additionally, you may use any data you like; I am using n = 20, ybar = 13, and the sample variance of y is 5.
   (soln 3, R code)
4. HW 4
   
5. Quiz Solutions
   

References

• The notes prepared by Prof. Joe Ibrahim are quite extensive and will be used to complement the text. These are available as a series of ps files from the BUGS Resources Link. Additionally, they have been converted to pdf files here. If you print these notes, please print at least two-up, i.e. two of the notes pages to every one side of a physical sheet of paper.
• Prof. Michael Lavine's "What is Bayesian statistics and why everything else is wrong"
• BUGS homepage
• R homepage
• Rat tumor data from GCSR chapter 5.
• Paper by Frank Dellaert that gives a nice description of the EM algorithm as successive lower bounds to the observed log-likelihood function.
• NCI's Jointpoint program.

Class Examples

Mar. 9

A WinBUGS implementation of the rat tumor example.

Mar. 2, 7

The puromycin example: lisp, WinBUGS. The lisp code uses the xlisp-stat function bayes-model, which has associated code for determining the second order Lapace approximation to marginal distributions. The marginal density plots for normal-gamma prior (independent normal priors on theta1 and theta2, gamma prior on tau) shown in class Mar. 7 were correct. The prior has more influence in this model than we might think, at first.

Feb. 21

The bioassay example in WinBUGS. We exported the data into R by using the "coda" button on the "sample monitor tool" available from the "inference" menu, saving the window that listed the iteration number and sampled value to a text file, and then reading this file by using the "read.table" command in R.

Feb. 16

"Intuition" for effective sample size.
Key references for MCMC convergence issues:

• Cowles, Mary Kathryn and Carlin, Bradley P. (1996). "Markov chain Monte Carlo convergence diagnostics: A comparative review," Journal of the American Statistical Association, 91, 883-904.
• Geyer (1992). Practical MCMC, Statistical Science, Vol. 7, No. 4., pp. 473-483 (and the discussion is critical!).

Feb. 14

R code for Gibbs sampling the binomial-beta-Poisson model. Associated R log file.

Feb. 7

R work.

Feb. 7.

The beta-binomial WinBUGS example.

model
{
y ~ dbin(p, n)
p ~ dbeta(alpha, beta)
}
data list(y = 8, n = 145, alpha = .5, beta = .5)
inits list(p = .5)

To load the model, highlight the word "model" and then click "check model" in the Specification Tool from the Model menu. To load the data, highlight the word "list" beginning the data and then click "load data" on the Specification Tool from the Model menu. Then compile using the Specification Tool. Then highlight the word "list" beginning the list of initial values for parameters and click "load inits" on the Specification Tool.

To run, use Inference -> Samples to bring up the Sample Monitor Tool. Type p in the node menu and then click set, to specify that we want to monitor the node p for the default of 1000000 iterations (this many iterations would be overkill for this simple model!). Bring up the Update tool from the Model -> update menu. Click "update" to run the default of 1000 iterations.

Now p has been monitored for these 1000 iterations and the values and various statistics about these values are available from the Sample Monitor Tool.