Computer Analysis of Data and Models: Diary

Week 1

I Contents

1. Introduction

2. Statistical MetaModels Toll Booth EG;

Morocco TB Data; Vaso Constriction Data

II Classical Methods

3. Random Variables

4. Fitting Parametric Distributions to Random Samples; Input Modelling

Normal Var Generator; Gamma Var Generator

5a. Maximum Likelihood Estimation

Likelihood Examples; Nelder Mead Method; NelderMeadDemo.

Lab 1 Study the Normal Var Generator/Gamma Var Generator examples.

Remind yourself of the terms pdf, cdf, inverse cdf.

How do the generators work?

Study the likelihood examples.

What form does the likelihood take for the toll booth data and the

Morocco data? What is the difference?

[If you have time: What form does it take for the Vaso constriction data?]

Study the Nelder Mead Method. Study the Nelder Mead Demo:

try different starting points, different objective functions..

Homework

Study the vaso constriction model (VasoConstrictionFit) and the form

the likelihood takes in this case.

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Week 2

5b. Maximum Likelihood Estimation Continued

GammaFitTollboothData and RegressionFitMorocco Gamma MLE

6. Accuracy of MLEs Gamma MLE; Regression Fit Morocco

III Computer Intensive Methods

7. Empirical Distribution Functions

8. Basic Bootstrap Method Bootstrap Median

Lab 2

Study how the likelihood is set up in the GammaFitTollboothData

and RegressionFitMorocco spreadsheets (see Worksheet 1)

Modify the RegressionFitMorocco example to analyse the

Traffic Queue data (see Worksheet 2).

Analyse the Cortisol Assay data (Worksheet 3).

Homework

Read the notes on EDF’s and study the Basic Bootstrap Method.

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Week 3

9. Evaluating the Distribution of MLEs by Bootstrapping Gamma Bootstrap

10. Comparing Samples Using the Basic Bootstrap Law and Kelton EG

11. The Parametric Bootstrap ParametricBS-GammaEG

Lab 3

Study how confidence intervals are calculated using bootstrapping.

Investigate the use of bootstrapping in the Toll Booth and

Morocco data examples.

Test out bootstrapping in the Traffic Queue and Cortisol Assay

examples (Worksheet 2 and Worksheet 3).

Homework

Read the Assignment Notes, and consider how the likelihood needs

to be set up for the problem.

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Week 4

12 Goodness of Fit Testing

12.1 Classical Goodness of Fit

12.2. Bootstrapping a GOF statistic

Gamma Fit Toll Booth Data; Normal Fit Toll Booth Data

13 Comparison of Different Models; Model Selection

Cement Data

14 Final Comments

Lab 4

Study the way goodness of fit is carried out using bootstrapping.

Run the spreadsheets that fit the gamma model and the normal model

to the toll booth data, and compare the fits using bootstrapping.

Study the Cement data ANOVA example.

Modify the cement data spreadsheet to analyse the Tyre Data

(see Worksheet 4).

Ask any questions you may have about the Assignment.