Page 240 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes 2. Biological processes running in a lake to simulate what could happen if these processes
were disturbed by external influences imposed on the model by the ………………
3. ……………… is a very expensive task in the latter, and in most cases it is even impossible
to generate long time series for individual or group behavior.
4. Successful simulation studies usually involve an artful mix of both ……………… and
exploration.

5. In a ……………… we might measure time in terms of the number of arrivals.
6. These ……………… arise in both observations from a single run and from independent
replications.
7. A common reference case for the SCV is an ……………… distribution.

8. Unlike the case of……………… we now face the problems of bias and dependence among
the random variables.
9. The ……………… helps us to determine if it is necessary to choose a special initial state or
delete an initial portion of the run.
10. ……………… of design rules taking into account fine details such as line-edge roughness.
11. The model is initialized with ……………… estimates of transition probabilities, age-
specific birth and death rates and so on.

12. The simulation is initialized with a ……………… distribution close to the empirical
distribution of 1950.
13. A simulation machine to predict the ……………… of real world experiments or perhaps to
replace such experiments.
14. In ……………… the model matches data before data are acquired from the real system.
15. Validation of ……………… is thus the same (or at least analogous) to validation of theories.

12.8 Review Questions

1. In your view simulations are controlled experiments. Give reasons.
2. The experimental design problem may not seem very difficult. Explain with a example.
3. Under very general regularity conditions, the long-run average coincides with the expected
value of the limiting steady-state distribution of the stochastic process. Comment.
4. What do you think as the difference between Bias, Mean Squared Error and Variance?
Discuss.

5. We also obtain relatively simple closed-form formulas when we establish diffusion-process
approximations via stochastic-process limits. Give examples.
6. Which is less time consuming Birth or Death Processes? Support your answer with proper
reasoning.
7. Find out the difference between quantitative and qualitative predictions.
8. Diffusion processes are continuous analogues of BD processes. Justify your answer.

9. “The run length required to make the bias suitably small is of the same order as the run
length required to make the width of a confidence interval suitably small.” Comments.
10. Diffusion processes are continuous analogues of BD processes. Elaborate.

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