NATCOR Design and Analysis of Simulation Experiments

Lab 1

1. Probability Distributions

 (i) Remind yourself of the terms pdf, cdf, inverse cdf.

(ii) Make charts of the pdf and cdf of the normal and gamma distributions.

(iii) Study the Normal Var Generator/Gamma Var Generator examples. How do

          the generators work?

     (iv) Construct a generator for the Weibull distribution.

2. Empirical Distribution Function

(i) In the the Normal Var Generator/Gamma Var Generator examples, add the graph of the PDF, appropriately scaled, to the frequency histogram chart

(ii) Make a chart of the EDF of the sample that is generated.

(iii) Add the CDF to the chart.

3. Statistical Metamodels

(i) Study the Toll Booth data and the Morocco data.

(ii) What is the appropriate statistical metamodel for each data set?

4. Nelder Mead Optimization

(Try out the Nelder-Mead optimization method on a few simple objective functions.

5. Statistical Metamodels

     (i) Study the Toll Booth data and the Morocco data.

     (ii) What is the appropriate statistical metamodel for each data set?

Lab 2

1. Maximum Likelihood Estimation

To carry out ML estimation one has to be able to write down the likelihood of the data.

     (i) Write down the likelihood for the examples given in the lectures.

     (ii) What is the likelihood for the Toll Booth Data and the Morocco Data?

One also has to be able to maximize the likelihood.

     (iii) Try out the Nelder-Mead optimization method on a few simple objective functions.

2. Fitting Metamodels

     (i) Study how ML estimation is used to fit metamodels to the toll booth and

Morocco data. (Refer to Worksheet 1 at the end of the lecture notes for help.)

3. Test the accuracy of MLE’s for the toll booth example and the Morocco data.

(Refer to Worksheet 1 at the end of the lecture notes for help.)

     (i) Calculate confidence intervals for the parameter estimates in each example,

          using the classical method.

     (ii) Calculate confidence intervals for the waiting performance index in the

          toll booth example.

     (iii) Calculate confidence intervals for the fitted regression function in the Morocco data example.

     (iv)  Repeat (ii) and (iii) only now use resampling methods.

4. Modify the Morocco Data Workbook to fit an appropriate metamodel to the

Traffic Queue Data.            Solution: RegressionFitTraffic

(Refer to Worksheet 2 at the end of the lecture notes for help.)

Extra Exercises. (There will not be time in the Labs or during the course to do these properly (unless you are very fast!). But you may wish to try these exercises at a later date.

1. Analyse the data here (Consult Worksheet 3): Cortisol Assay

Test out bootstrapping in the Traffic Queue and Cortisol Assay examples

     (Worksheet 2 and Worksheet 3).

2.  Study the Cement data ANOVA example.

     Modify the cement data spreadsheet to analyse the data here: Tyre Data

     (see Worksheet 4).