1. National Public Health Institute, Finland www.ktl.fi Open risk assessment Lecture 4: Defining variables Jouni Tuomisto KTL, Finland

2. National Public Health Institute, Finland www.ktl.fi Lecture contents Probabilistic interpretation of variables Joint and conditional distributions Attributes Sub-attributes Data relations vs. causal relations Scenarios and their use

3. National Public Health Institute, Finland www.ktl.fi Probability distribution P(A) ‏

4. National Public Health Institute, Finland www.ktl.fi P(B) ‏

5. National Public Health Institute, Finland www.ktl.fi Joint distribution P(A,B) ‏

6. National Public Health Institute, Finland www.ktl.fi P(C) ‏

7. National Public Health Institute, Finland www.ktl.fi Joint distribution P(B,C) ‏ Conditional probability distributions P(B|C)‏ P(C|B)‏

8. National Public Health Institute, Finland www.ktl.fi Priors and posteriors A falsification process

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12. National Public Health Institute, Finland www.ktl.fi 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) ‏

13. National Public Health Institute, Finland www.ktl.fi 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 CommentsQuestion to be answered Sub- attributes Attribute

14. National Public Health Institute, Finland www.ktl.fi Connections between variable attributes

15. National Public Health Institute, Finland www.ktl.fi Causal relations Judea Pearl Statistics is NOT only about associations. Causal relations can be studied empirically using the do operator.

16. National Public Health Institute, Finland www.ktl.fi 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

17. National Public Health Institute, Finland www.ktl.fi 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

18. National Public Health Institute, Finland www.ktl.fi 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.

19. National Public Health Institute, Finland www.ktl.fi 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