Statistical Modelling and Causality

Federica Russo*, Michel Mouchart**, Michel Ghins*, Guillaume Wunsch***

* Institut Supérieur de Philosophie, Université Catholique de Louvain** Institut de Statistique, Université Catholique de Louvain*** Institut de Démographie, Université Catholique de Louvain

Structure of the paper Scientific knowledge Data Causality and statistical modelling

The statistical model Statistical inference and structural models Conditional models and exogeneity Beyond exogeneity Hypothetico-deductive methodology

The population and the individual

Scientific knowledge We are moderate realists:

Models grant cognitive access to some unobservable parts of reality

Modelling is constructing a simplifiedrepresentation of a complex reality

Data To acquire causal knowledge

we try to make sense of observations

However, collecting data isproblematic under several respects

Causality and statistical modelling The statistical model

A stochastic representation of the world Analyze data asas a realization

of a family of distributions

Causality and statistical modelling Statistical inference and structural models

Structural models make statistical inferenceoperational and meaningfulthrough a learning-by-observinglearning-by-observing process

StructuralStructural models: a representation of theworld that is stable under a large classof interventions

Causality and statistical modelling Conditional models and exogeneity

p (x | ) = p (z | ) p (y | z , )

The conditional part is structuralstructural and represents the data generating process

Z is an exogenousexogenous variable in a structural model,that is Z is a causalcausal variable

Causality and statistical modelling

Causality: exogeneity in a structural model

operational concept, internal to the model

Beyond exogeneity

Temporal and atemporal features grant causality

Hypothetico-deductive methodology Theorizing out-of-sample information

Choice of variablesFormulation of the causal hypothesis

Iteratively: Building the statistical model Testing the adequacy model-data

The population and the individual Methodological issue:

Detect causal variables, provide a sufficient list Describe the causal mechanism

Practical issue: Take decisions about individualsindividuals

based on knowledge about the populationpopulation

Epistemological issue: Causal knowledge about the population

guides causal attribution about individualsthrough Bayes’ theorem

To conclude… Causality: exogeneityexogeneity in a structural model

Thus defined, causality is internalinternal to the model

Structural models mediateepistemic accessepistemic access to causal relations