# STA 410, ASSIGNMENT 4, SPRING 2004.

The data for the assignment is as follows:

> cbind(x,y)
       x y
[1,] 0.5 4
[2,] 2.2 8
[3,] 1.2 2
[4,] 2.0 6
[5,] 0.7 2
[6,] 0.2 1

Here are the results, for models H1, H2, and H3:

> H1(x,y,10)
$marg.lik
[1] 1.957519e-07

$E1
[1] 4.000261

> H1(x,y,20)
$marg.lik
[1] 1.957673e-07

$E1
[1] 4

> H2(x,y,10)
$marg.lik
[1] 5.83287e-06

$E1
[1] 3.472166

> H2(x,y,20)
$marg.lik
[1] 5.832912e-06

$E1
[1] 3.472158

> H3(x,y,10)
$marg.lik
[1] 5.065307e-06

$E1
[1] 3.813497

> H3(x,y,20)
$marg.lik
[1] 5.065313e-06

$E1
[1] 3.8135


We can see that 20 points is enough for Simpson's Rule for this
problem, since the results are almost the same with only 10 points.
The marginal likelihoods are as follows:

  H1: 1.96e-7
  H2: 5.83e-6
  H3: 5.07e-6

The data prefer H3 over H1 by a factor of 5.07e-6/1.96e-7 = 26.  This
is big enough that we might well decide that H1 can be almost ruled
out - ie, one can be pretty sure that BSE is a cause of nvCJD,
assuming other aspects of the study allow this conclusion (eg, there
are no confounding factors), and that we don't have any strong prior
beliefs about whether BSE is a cause or not.  The marginal likelihoods
for H2 and H3 are almost the same, however, so the data don't provide
enough evidence for us to decide whether or not there is another cause
of nvCJD in addition to BSE.