1. Probability and Causality in the Social Sciences Federica RussoCenter Leo Apostel, VrijeUniversiteitBrussel& Centre for Reasoning, University of Kent

2. Overview:Probability: syntax and semanticsProbability: my preferred perspective (Old) results, very brieflyNew ideas in progress Dispersion and variation Individual and population 2

3. PROBABILITY:SYNTAX AND SEMANTICS 3

4. A metaphorSyntax: axiomatisation Kolmogorov, by and large acceptedSemantics: interpretation 3 major schools: Logicist Physical (frequentist and propensity) Epistemic interpretation (Bayesian) 4

5. One approach to probabilityWhat is the meaning of probability? Not in an absolute sense But relatively to a given scientific contextFor instance Emigration rates in a region and propensity of farmers migrate (wrt other occupations) The probability that my gastric ulcer is due to HelycobacterPilori rather than stress given positive results at the test 5

6. How I got to probabilityAccounts of causalityProbabilisticaccounts of causality Accounts of probabilityStatistical studies of populationsProbabilistic models Accounts of probability 6

7. The philosophicalThe empirical problem of problem of causality causality Probabilistic models in social science Probability and causality in the social sciences 7

8. A TASTE OF ARGUMENTSPREVIOUSLY DEVELOPED 8

9. Janus-faced probabilityA long history, since Pascal and Laplace; the duality emerged later; plans for unificationsWhos in the drivers sit? Frequency-driven epistemic probabilities Degrees of belief are shaped upon knowledge of frequencies Credence-driven physical probabilities Credence in the truth of a proposition fixes the chance of the event (as long as evidence does not contradict) 9

10. Frequency-driven epistemic probabilitiesAccount for different types of probabilistic causal claims because they are Janus-facedMake sense of learning from experience because they incorporate empirical constraints 10

11. Objective Bayesianism and hypothesis testingHypothesis testing compares hypotheses with data Null hypothesis: observed variation is chancy Alternative hypothesis: observed variation is real Test statistic Null hypothesis is accepted/rejected depending on the chosen p-value 11

12. Probability in hypothesis testingEvaluate the probability to obtain the sample if the hypothesis is true The probability of a hypothesis is single-case Meaningful for Bayesians, meaningless for frequentistsProbability of which hypothesis? Null or alternative? Objective Bayesianism treats them on equal footing, unless evidence suggests otherwise A problem of evidence, not of type of error 12

13. NEW IDEAS TO BE DEVELOPED 13

14. Suggested readingDaniel CourgeauProbability andSocial Science(Springer, 2012)For the philosopher ofprobability interested inprobabilistic approaches insocial scienceFor the practicing socialscientists interested in thefoundations of probability 14

15. DISPERSION AND VARIATION 15

16. Population science studies Births, deaths, and migration flows which affects the population.The probability of fertility, mortality and migration [Courgeau 2012, 198]A tight knot between probability and modellingin population science 16

17. Dispersion2 meanings of dispersion PROB: Spread of observations around their central value. Measured by e.g. variance, standard deviation, variation coefficient SOCSC: As heterogeneity, in sub-populations the variables mean and variance are strongly dispersedCourgeau: a historical reconstruction of how dispersionPROB,SOCSCis used in various methods in population scienceHere: bring these arguments a step forward Why is dispersion so important? From descriptive to causal analysis 17

18. VariationIn reasoning aboutcause-effectrelations, what notionguides this reasoning?Regularity?Invariance?Production? ...Hunting for a rationale 18

19. Rationale vsdefinitionRationale: a principle/notion/concept underlying decision/reasoning/modellingDefinition: A description of a thing by means of its properties or if its functionHere: hunting for the notion underlying model building and model testing: rationale, not definition 19

20. Variation in causal modelsIf we had to be precise: A statistical model in the form of a set of probability distributions A vector X of variables; A vector of parameters A decomposition of X in a sequence of marginal and conditional components well take the shortcut 20

21. Variation in structural models Consider a structural equation Y = X+Are there meaningful co-variations between X and Y? Are these variations chancy or causal? hypothesis testing; invariance; exogeneity 21

22. Dispersion VariationA purely probabilistic The analogue concept description of the regimenting causal population analysisPROB: How observations are How the probability of a spread around a value variables changes withSOCSC: How variables other variables change parameters are dispersed in sub-populations 22

23. INDIVIDUAL AND POPULATION 23

24. The concept of populationAggregate of individuals which conform to a given definition [Ryder 1964, quoted in Courgeau 2012, p. 196] Spatial and temporal specificity Example criteria: political, economic, religious, social, Overlapping populationsHere, physical probability, mainly frequentistMeasure general characteristics of groups 24

25. The concept of individualIndividuals in a population Only a small number of phenomena and of characteristics of these individuals We shall create an abstract fictitious individual, the statistical individual, as distinct from the observed individual. The statistical individual will experience event that obey the axioms of probability theory chosen to treat the observations [Courgeau 2012, p.197]Thus we can also study individual-level data (and the effects of aggregate characteristics on them) 25

26. How can we go back to the observed individual?Actuarial cases How much should my car insurance be?Socio-economic intervention How likely is this unemployment programme to work for Mr Rossi?Epidemiology and medicine If I take contraceptive pill X, will Idevelop thrombosis? Did working at Eternit cause Mr Rossi and Mr Bianchi to develop lung cancer? 26

27. The population to help the individual?How can we combine knowledge of aggregates to calculate single-case probabilities?Objective Bayesianism: Degrees of beliefs should be probabilistic, calibrated with evidence, and otherwise equivocal. [Williamson 2010] 27

28. To sum upMany ways of looking at probability the one I like: What probability in a given scientific context?In the past, explored links between frequencies and objective Bayesianism To have a grip on empirical data To revisit hypothesis testingCourgeaus book prompts new paths of research Dispersion and variation Statistical individual, population, and observed individual 28

29. To concludeAn exercise that shows Useful interactions between probability theory, population science, and philosophy How intertwined descriptive and causal analysis are How much abstract theory and empirical data help each other in constructing knowledge 29