Once again about the science-policy interface

1. Once again about the science-policy interface

2. Q R A Open risk management: overview

3. Human-human interface • There are really interesting new interfaces for transmitting information from person to person: • Facebook: How are you? • Wikipedia: What is thing X? • Opasnet: What should we do? • A universal interface for communication about decisions and decision support is urgently needed. • When that problem is solved, the communication problem between science and policy is solved as well. There is no need for a separate science-policy interface.

4. Introduction to probability theory Jouni Tuomisto THL

5. Probability of a red ball • P(x|K) = R/N, • x=event that a red ball is picked • K=your knowledge about the situation

6. Probability of an event x Prize p Red Red ball 100 € • If you are indifferent between decisions 1 and 2, then your probability of x is p=R/N. Decision 1 White ball 0 € 1-p x happens 100 € Decision 2 0 € x does not happen

7. The meaning of uncertainty • Uncertainty is that which disappears when we become certain. • We become certain of a declarative sentence when (a) truth conditions exist and (b) the conditions for the value ‘true’ hold. • (Bedford and Cooke 2001) • Truth conditions: • It is possible to design a setting where it can be observed whether the truth conditions are met or not.

8. Different kinds of uncertainty • Aleatory (variability, irreducible) • Epistemic (reducible), actually the difference only depends on its purpose in a model. • Weights of individuals is aleatory if we are interested in each person, but epistemic if we are interested in a random person in the population. • Parameter (in a model): should be observable! • Model: several models can be treated as parameters in a meta-model

9. Different kinds of uncertainty: not really uncertainty • Ambiguity: not uncertainty but fuzziness of description • Volitional uncertainty: “The probability that I will clean up the basement next weekend.” • Uncertainties about own actions cannot be measured by probabilities.

10. What is probability? • 1. Frequentists talk about probabilities only when dealing with experiments that are random and well-defined. The probability of a random event denotes the relative frequency of occurrence of an experiment's outcome, when repeating the experiment. Frequentists consider probability to be the relative frequency "in the long run" of outcomes.[1] • 2. Bayesians, however, assign probabilities to any statement whatsoever, even when no random process is involved. Probability, for a Bayesian, is a way to represent an individual's degree of belief in a statement, or an objective degree of rational belief, given the evidence. • Source: Wikipedia

11. Probability rules • Rule 1 (convexity): • For all A and B, 0 ≤ P(A|B) ≤ 1 and P(A|A)=1. • Cromwell’s rule P(A|B)=1 if and only if A is a logical consequence of B. • Rule 2 (addition): if A and B are exclusive, given C, • P(A U B|C) = P(A|C) + P(B|C). • P(A U B|C) = P(A|C) + P(B|C) – P(A ∩ B|C) if not exclusive. • Rule 3 (multiplication): for all A, B, and C, • P(AB|C) = P(A|BC) P(B|C) • Rule 4 (conglomerability): if {Bn} is a partition, possibly infinite, of C and P(A|BnC)=k, the same value for all n, then P(A|C)=k.

12. Conditional probabilities • The totality of possible states of the world P(A) P(B)

13. Binomial distribution • You make n trials with success probability p. The number of successful trials k follows the binomial distribution. • Like drawing n balls (with replacement) from an urn and k being red. • P(n,k|p) = n!/k!/(n-k)! pk (1-p)(n-k)

14. Example • You draw randomly 3 balls from an urn with 40 red and 60 white balls. What is the probability distribution for the number of red balls?

15. Answer • P(n,k|p) = n!/k!/(n-k)! pk (1-p)(n-k) • 0 red: 3!/0!/3! *0.40*(1-0.4)3-0 • = 1*1*0.63 = 0.216 • 1 red: 3!/1!/2! *0.41*(1-0.4)3-1 = 0.432 • 2 red: 3!/2!/2! *0.42*(1-0.4)3-2 = 0.288 • 3 red: 3!/3!/0! *0.43*(1-0.4)3-3 = 0.064

16. Binomial distribution (n=6)

17. Binomial distribution: likelihoods