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CPS1110 Selamawit M. et al.
of the band width on posterior model, we have used three different level of
band width which are low, optimum, and high respectively. Their performance
are tested on prediction from the posterior model. The prediction will actually
heavily depend on the choice of band width. The effect of varying band width
on the circular uniform kernel likelihood model is illustrated in Fig.2. It has two
parts, the upper part contains contour plots of the likelihood model for each
soil class made from the circular uniform kernel while the lower part contains
posterior model result based on the trend prior model and the corresponding
likelihood model.
The reference profile , observations , the prior marginal pdf profile,
0

the MAP, MMAP, and the posterior probability profile are presented in the

lower display going from left to right respectively. Seven realizations which are
sampled from the posterior pdf are also presented in the lower display in the
same figure. The MAP, MMAP, and posterior marginal pdf based on circular
uniform kernel likelihood model with optimum band width are presented in
the upper right of Fig.2b. The prediction largely appear with the correct
sequence of the classes compared to the true profile at the top left in the same
figure. However, there appears to be some overlaps of the classes. For
example, the red class is predicted in approximately half of the blue class at
the bottom of the profile. The main reason for this may be found in the
likelihood model. The red classes have masked some part of the blue classes.
Observe also the bimodality in the likelihood model, see Fig.1b and 2a. The
corresponding realization in the bottom line of Fig.2b are fairly similar, and
display little uncertainty, resulting from the bimodal likelihood model see
Fig.2a.

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