BAYESIAN NON-LINEAR MODELS

ASSIGNMENT 6

BAYESIAN NON-LINEAR MODELS

The following contingency table was also given in assignments 2 and 3.

In the following contingency table we have 79 patients cross-classified by three factors: A= the condition of the patient, B = whether the patient received antitoxin or not and C = whether the patient survived or not. Prime interest is given on the effect of antitoxin to deaths from tetanus.

Read the following papers

• Bayesian Variable Selection Using the Gibbs Sampler 
• On Bayesian Model and Variable Selection Using MCMC.
• Gibbs Variable Selection Using BUGS.

and then calculate the posterior model probabilities using SSVS and GVS for the logit link. Use the appropriate priors for f(β_i | γ_i=1 ) , pseudoprior f(β_i | γ_i=0 ) and for f( γ_i ).

Write a brief answer to the following questions:

1. How would you select the prior variance of each β_i? How sensitive are the two methods on the choice of the prior variance?
2. Interpret the results from SSVS and GVS. Are they different? Why are they different?
3. Produce a diagram of the residuals for a prior distribution.
4. What model do you think that we should choose?
5. Is there any connection of SSVS, GVS and Reversible Jump. Explain briefly. Which of the 3 method is more flexible and why.

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Last revised: 13-5-1999