# A group of n students sit two exams. Exam one is on history and exam two is

## Question:

A group of n students sit two exams. Exam one is on history and exam two is on chemistry. Let x_{i} and y_{i} denote the ith student's score in the history and chemistry exams, respectively. The following linear regression model is proposed for the relationship between the two exam scores:

where ε_{i }~ N(O, 1/τ).

Assume that x = (x_{1}, x_{2} , ... , X_{n}) and y = (y_{1}, y_{2} , ... , Y_{n}) and that a, β and τ are unknown parameters to be estimated.

Describe a reversible jump MCMC algorithm including discussion of the acceptance probability, to move between the four competing models:

Note that if z is a random variable with probability density function f given by

then z ~ N(B, 1/ A) [due to P. Neal].

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