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Open risk assessment Lecture 4: Defining variables

Jouni TuomistoKTL, Finland

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Lecture contents• Probabilistic interpretation of variables• Joint and conditional distributions• Attributes• Sub-attributes• Data relations vs. causal relations• Scenarios and their use

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•Probability distribution P(A)

0 1 0 2 0 3 0 4 05 1 5 2 5 3 50

0 .1

0 .2

0 .3

0 .4

0 .0 5

0 .1 5

0 .2 5

0 .3 5

Variable A

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P(B)

10 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .90

1

2

3

0 .5

1 .5

2 .5

3 .5

Variable B

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Joint distribution P(A,B)

0 1 0 2 0 3 05 1 5 2 5

1

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

Variable A

Va

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B

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P(C)

1 2 31 .5 2 .5 3 .50 .7 5 1 .2 5 1 .7 5 2 .2 5 2 .7 5 3 .2 5 3 .7 50

1

2

3

0 .5

1 .5

2 .5

Variable C

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10 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9

1

2

3

0 .8

1 .2

1 .4

1 .6

1 .8

2 .2

2 .4

2 .6

2 .8

3 .2

Variable B

Va

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CJoint distribution P(B,C)

• Conditional probability distributions

P(B|C)

P(C|B)

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Priors and posteriors

0 1 0 2 05 1 5-2 .5 2 .5 7 .5 1 2 .5 1 7 .5 2 2 .50

1

2

0 .5

1 .5

2 .5

0 .2 5

0 .7 5

1 .2 5

1 .7 5

2 .2 5

2 .7 5

Variable C

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Var iable CU n in fo rm a tive p rio r P rio r 2 P o s te rio r

• A falsification process

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Conditional probabilities in the causal diagram

• The causal diagram is actually a large joint distribution

• A variable is described as a conditional probability: P(variable|upstream variables)

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Attributes and subattributes of a variable

If possible, a numerical expression or distribution.

What is the answer to the question defined in the scope? Result

The definition uses algebra or other explicit methods if possible.

How can you derive or calculate the answer?

•Causality •Data •Unit•Formula

Definition

This includes a verbal definition of the spatial, temporal, and other limits (system boundaries) of the variable. The scope is defined according to the use purpose of the assessment(s) that the variable belongs to.

What is the question to which the variable answers? Scope

Two variables must not have identical names.

What is the name of the variable? Name

Comments Question to be answered Sub-attributes Attribute

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Connections between variable attributes

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•Causal relations• Judea Pearl• Statistics is NOT only

about associations. Causal relations can be studied empirically using the do operator.

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•Data relations vs. causal relations• Causal relation: the variable result

changes if the upstream variable is manipulated (do operator)

• Data relation: a piece of data or a variable gives information about the variable of interest, but the manipulation does not change the result–PM2.5 concentration in Stockholm vs.

in Helsinki

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•Scenario• Scenario: the result of a variable is (temporally for

an assessment) set to a particular value or range irrespective of its true value. A scenario may contain several such manipulations.

• Purpose: – To make the assessment more interesting– To avoid excessive work on variables that are not of

interest or importance in the assessment

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Index• Index: a list of particular values that are along a

dimension used for a variable. This list is used in practical calculations in the assessment.– Longitude and latitude are geographical dimensions– [0, 1, 2, 3, 4] degrees of longitude is an index that can

be used in an assessment.– Another assessment may use another index for the

same dimension.

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Parts of an attribute• Actual content: what is known• Narrative description: any explanations or

background information that is useful to understand the actual content

• Discussion: (formal) discussions about the actual content