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CPS1110 Selamawit M. et al.

(a) Likelihood Model: Circular Uniform Kernel with Optimal
bandwidth r=0.2

(b) Results from Trend Prior Model
Figure 2: Results from Bayesian Inversion of Case Study

(a) Likelihood Model: Gaussian Kernel with Optimal Band width

(b) Result from Trend Prior Model
Figure 3: Results from Bayesian Inversion of Case Study

Fig.3 contain results from the trend prior model with the Gaussian kernel
likelihood model. The lay-out of the figure is the same as for Fig.2.

The predictions, MAP, MMAP, and posterior marginal pdf based on Gaussian
kernel likelihood model with optimum band width are presented in Fig.3b. The
inversion results are not very reliable since the blue class seems to replace the red
class. The red class is almost not present. The posterior realizations displayed in the
bottom line appears with little variability. 5. Conclusions Bayesian inversion for
prediction of sub-surface facies profile based on the observed well log
observations is made. The posterior model is assessed by the Forward-Backward
and Viterbi algorithms.
For prediction of the sub-surface layer, both circular uniform kernel and
Gaussian kernel likelihood model are defined and evaluated. The model parameter
band width in the kernel likelihood is estimated by a cross-validation psuedo-

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