Final exam, CS 5353, Fall 2008

Date: Tuesday, December 9, 2008.

Name (please print): ___________________________________________________________________________________

1. Motivations.

2. Statistical foundations.
Assume that the probability p(A) of the event A is 0.6, and the probability p(B) of the event B is 0.5.

3. Mathematical techniques.

Provide an example where both Maximum Likelihood Method and bisection are used in estimating uncertainty of the result of data processing.

4. Data fusion.
Let us assume that we have measured the same quantity with two different measurement instruments. The result of the first measurement is 1.2, the result of the second measurement is 0.8. Combine these two results into a single "fused" value, in the following two situations:

Where do the formulas that you used come from (no need for detailed derivations, just explain the main ideas.)

5. Linearization.

6. Uncertainty in data processing: computational aspects.
For the formulas for computing uncertainty of the result of data processing, explain how the computational complexity (= number of computational steps) depends on the choice of the parameters hi used in numerical differentiation, and what is the choice for which the computational complexity is the smallest:

7. Uncertainty in data processing: Monte-Carlo method.
Explain why Monte-Carlo method is useful in estimating uncertainty of the result of data processing, and for what number of inputs it is useful:

Provide a numerical example of the number of iterations that are needed to achieve a given accuracy.

8. Estimating reliability and trust: Monte-Carlo method.

9. Reliability.
On the example of each of the following two cases:

estimate two values:

10. Describe the contents of one of the class projects -- different from your own project.