Question-1
Using the definitions of expectation, conditional expectation and distribution functions, derive the equations for optimal transformation for the bivariate case (Eqs. 6 and 7 in SPE 35412).
Question-2
- For the (synthetic data) set provided, write a program to generate the optimal non-parametric transformations of the data using the ACE algorithm.
- Use at least three different smoothers to demonstrate the role of smoothing algorithms in non-parametric regression.
- Select your ‘best’ smoother. Now change the span size to illustrate the bias-variance trade-off. Clearly explain what is meant by the bias-variance trade-off.
Question-3
For the given data for the Salt Creek Field Unit, you are to develop a correlation between permeability (or log permeability) and well logs using non-parametric regression. Use the software GRACE to perform the following: - Use the following seven well logs to build your correlation: GR, LLD, MSFL, DT, RHOB, NPHI and PEF. Build your correlation for two lithotypes: 7 and 8. Starting with all the well logs, you need to go through a variable selection procedure to come up with the ‘best ‘correlation to predict permeability from well logs.
- You are also given the data for a ‘blind’ well (G517) that was not used in building the correlation. Predict the permeability for the corresponding lithotypes.
- Compare the results from your correlation with the measured permeability.
- Summarize your results.