Probability, statistics, and the likelihood ratio for non-experts [draft]
Preface
Why this book?
Who this is for
How to contribute
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Acknowledgements
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Contributors
Software
Updates and versions
About this version (version 1.0)
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Future content
1
Introduction
2
Uncertainty
2.1
What we mean by
uncertainty
2.2
Types of uncertainty
2.3
Uncertainty in scientific evidence
2.4
Example: fibre interpretation
2.5
Drag and Drop: uncertainty
2.6
Communicating uncertainty
2.7
Summary: uncertainty
3
Probability to describe uncertainty
3.1
Quantifying uncertainty
3.2
Example: coin toss
3.3
Interactive coin toss
3.4
Personal probabilities
3.5
Conditioning on information
3.6
Conditioning on the past and future
3.7
Example: double coin toss
3.8
Interactive double coin toss
3.9
Example: coin toss game
3.10
Odds
3.11
Bayes’ rule
3.12
Example: guessing coin 1
3.13
Coin guess without Bayes’ rule
3.14
Coin guess using Bayes’ rule
3.15
Reliable probabilities
3.16
Base rates and error rates
3.17
Example: diagnostic tests
3.18
Interactive disease testing
3.19
Example: doping
3.20
Interactive doping
3.21
Summary: probability
3.22
More information
4
Propositions to frame uncertainty
4.1
Facts-in-issue
4.2
Propositions
4.3
Competing propositions
4.4
Case scenario: forming propositions
4.5
Proposition properties
4.6
Example: exhaustivity and mutual exclusivity
4.7
Hierarchy of propositions
4.8
Offense level propositions
4.9
Activity level propositions
4.10
Source level propositions
4.11
Sub-source level propositions
4.12
Example: proposition levels
4.13
Probative value of evidence
4.14
Example: probative value
4.15
Changing propositions
4.16
Probabilities for propositions
4.17
Summary: propositions
5
Likelihood ratio to evaluate uncertainty
5.1
Relative support for competing propositions
5.2
Quantifying probative value
5.3
LR calculator
5.4
Example: DNA match
5.5
DNA match LR
5.6
Updating odds
5.7
Example: doping (revisited)
5.8
Doping LR
5.9
Doping posterior odds
5.10
Interactive doping LR
5.11
Combining evidence
5.12
Serial evidence schemes
5.13
Parallel evidence schemes
5.14
Robustness
5.15
Communication
5.16
Summary: likelihood ratio
References
Copyright © 2020-2021 LRCFS
Probability, statistics, and the likelihood ratio for non-experts [1st Edition]
4.12
Example: proposition levels
Practice identifying the correct proposition level with the examples below.