Dstl
Workshop on Statistical Uncertainty 23 November 2009
These notes are drawn from
those of a NATCOR taught course on statistical modelling.
The material available covers
both classical methods of analysis and computer intensive resampling methods.
The first dstl workshop will
cover classical methods of statistical analysis.
The computer intensive methods
will be covered in a second workshop.
The lectures are based on Working
Notes covering the following:
I
Statistical Metamodels
1.
Introduction
2.
Statistical MetaModels
II
Classical Methods
3.
Random Variables
4.
Fitting Parametric Distributions to Random Samples; Input Modelling
5.
Maximum Likelihood Estimation
6.
Accuracy of MLEs
III
Computer Intensive Methods
7.
Empirical Distribution Functions
8.
Basic Bootstrap Method
9.
Evaluating the Distribution of MLEs by Bootstrapping
10.
Comparing Samples Using the Basic Bootstrap
11.
The Parametric Bootstrap
12
Goodness of Fit Testing
12.1
Classical
Goodness of Fit
12.2.
Bootstrapping a GOF statistic
13
Comparison of Different Models; Model Selection
IV
Design of Experiments
14.
Linear Regression Metamodels
15.
Fitting and Assessing the Linear Model
15.1
Least Squares Estimation
15.2
ANOVA
15.3
Individual Coefficients
16 Prediction
with the Linear Model
17 Additional
Explanatory Variables
18
Experimental Designs
18.1
Main Effects Model
18.1.1
Factorial Design
18.1.2
Plackett-Burman Designs
19
Interactions
20
Central Composite Designs
21
Comments on Design of Experiments
22
Final Comments
You can access the working notes
by clicking on the links given below. The Working Notes are meant to be worked
through.
They contain Examples and
Exercises. These illustrate the topic or method being discussed. They are
an essential part of the text and must be carefully studied.
Many of the Examples and
Exercises come with their own link. (i) Some of the links contain additional
notes and more detailed formulas, (ii) The other links are to actual
spreadsheets containing data and the worked details using the data.
Some of the initial
spreadsheets contain elementary exercises connected with generating random
variables and simple sampling experiments. You should aim to do these exercises
yourself independently of the worked solutions and then compare your solution
with that supplied. The point of these exercises is to give you familiarity
with basic formulas and functions that you will need for the more complicated
later examples.
The other spreadsheets contain
more substantial problems. These are solved using VBA macros for carrying out
more substantial calculations and more extensive analyses. You are not
expected to write your own macros to duplicate these macros. However you should
spend sufficient time using and studying the macros to understand how they
function. Thus you should aim to be able to understand the workings of
the VBA macros sufficiently well to be able to modify them for solving simple
variations of the problem to which they have presently been applied. I
have tried to make the macros transparent and relatively easy to modify.
In the spreadsheets, the
following convention for cells is used:
Cells with a Yellow background
- Headings, Incidental Information
Cells with a Green background
- Input Information used in calculations on that Sheet
Intermediate Results and
Calculations are not usually coloured.
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Links
• Lectures/Labs Diary
Lab WorkSheets
References are provided in the
Course Profile and at the end of Part IV
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Stop Press
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