Graduate Training Programme
————————————————————————————
Computer Intensive Analysis
of Data and Models
The course comprises three
main components:
(i) Working Notes: These
contain the material covered in
the lectures. This has a strong practical emphasis.
(ii)
Worked Examples: These are
spreadsheet examples. They are embedded in the Working Notes.
(iii)
Technical
Notes: These cover the theoretical foundations of bootstrapping.
————————————————————————————
The
Working notes cover the following:
I Introduction
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
14 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 need to be 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. The point of these exercises is to
remind you of the basic formulas and functions that you will need for the more
complicated later examples. You should already be familiar with this material.
However you might wish to spend a short time checking that you do know this
material well.
The other spreadsheets
contain more substantial problems.
These are solved using VBA
macros for carrying out more substantial calculations and more extensive
analyses. The macros are fairly generic in that they only need minor adjustment
to solve other similar problems.
The main reason for using
such macros is to demonstrate that the structure of many problems follows a
similar pattern, depending on the solution of a limited number of standard
problems.
You are expected to follow
the working of the macros in sufficient detail to appreciate this and to be
able to make the minor changes to them to solve similar problems.
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.
————————————————————————————
The Technical Notes cover
the following
1. The Bootstrap
The Bootstrap Concept
Basic Method
The Double Bootstrap and Bias Correction
Parametric Bootstrap
2. Percentiles and Confidence Intervals
Percentiles
Confidence Intervals by Direct Bootstrapping
Studentization
Percentile Methods
3. Theory
Convergence Rates
Asymptotic Accuracy of EDF's
Asymptotic Accuracy of Confidence Intervals
Failure of Bootstrapping
4. Monte-Carlo/Simulation Models
Direct Models
Metamodels
Linear Metamodels
NonLinear Metamodels
Uses of Metamodels
Metamodel Comparison and Selection
5. Bootstrap Comparisons
Goodness-of-Fit and Validation
Comparison of Different Systems
6. Bayesian Models
7. Time Series Output
Residual Sampling
Block Sampling
Spectral resampling
8. Final Comment
————————————————————————————
Links
References are at the end of
the Technical Notes (some references also at the end of Part III of the Working
Notes).
————————————————————————————
Synopsis of Lectures
Lecture #1
W1. Introduction
W2.
Statistical MetaModels.
W3. Random Variables
W4.
Fitting Parametric Distributions to Random Samples; Input Modelling
Lecture #2
W5. Maximum
Likelihood Estimation
W6. Accuracy of ML Estimators
Lecture #3
W7. Empirical Distribution Functions
W8. Basic Bootstrap
Method
W9. Evaluating the Distribution of MLEs by
Bootstrapping
Lab #1
Examine examples of Lectures 1, 2 and 3
Lecture #4
T1 The Bootstrap
T1.1 The Bootstrap Concept
T1.2 Basic
Method
T1.3 The
Double Bootstrap and Bias Correction
T2 Percentiles
Lecture #5
W11. The Parametric Bootstrap
T4.2 Metamodels
T4.3
Linear Metamodels
T4.4
Nonlinear Metamodels
Lab #2
Examine examples of Lectures 3 and 5
Fit a suitable model to the Traffic Queue and Cortisol Assay Data
Lecture #6
W12 Goodness of
Fit Testing
T5.1
Goodness-Of-Fit and Validation
Lecture #7
W10 Comparing
Samples Using the Basic Bootstrap
W13 Comparison of
Different Models; Model Selection
T4.6 Metamodel
Comparison and Selection
Lecture #8
T3 Theory
T3.1 Convergence
Rates
T3.2 Asymptotic Accuracy
of EDF’s
T3.3 Asymptotic
Accuracy of Confidence Intervals
T3.4 Failure of
Bootstrapping
W14 Final Comments
Lab #3
Examine examples of Lectures 6 and 7
Particular data sets you may wish to consider are
(i) ANOVA analysis of Tyre Wear Data
(ii) An analysis of Component Lifetimes. For this problem
there
are some accompanying notes you should read first
to
help you: Component lifetime
Notes
………………………………………………………………………………………………..