Causal risk models of air transport - NLR-ATSI

Notice also that P(A|C) does not necessarily imply that A is the effect and C is the cause.
Take the example A = car does not start, C = empty fuel tank. Both P(A|C) and P(C|A)
exist. In order to be able to differentiate between cause and effect there must be additional
information on the direction of the relation between C and A. In a causal model this
direction is indicated by a directed edge (see section 3.7).
3.3. Causation to predict the future
One of the main reasons why we are interested in causation is because it allows us to
predict system behaviour if we assume that the past and present determine the future.
Among the first scientists to seriously address this issue were the German philosopher
Immanuel Kant (1724-1804) and the French mathematician Pierre Simon Laplace (1749-
1827). Kant stated that every effect has a cause which is a prior event and that this cause
effect relation is ‘fixed’. Therefore, if we have observed, in the past, that certain causes
have certain effects we can assume that the same causes will have the same effects in the
future [Kant 1781]. Laplace went even further when he published his theory of scientific
determinism. He wrote [Laplace 1814]:
"We may regard the present state of the universe as the effect of its past and the cause
of its future. An intellect which at any given moment knew all of the forces that animate
nature and the mutual positions of the beings that compose it, if this intellect were vast
enough to submit the data to analysis, could condense into a single formula the
movement of the greatest bodies of the universe and that of the lightest atom; for such
an intellect nothing could be uncertain and the future just like the past would be
present before its eyes."
According to Laplace’s conception of nature, all laws in nature are deterministic, and
randomness surfaces merely due to our ignorance of the underlying boundary conditions
[Pearl 2000b]. Werner Heisenberg‘s (1901-1976) uncertainty principle shows that Laplace's
vision, of a complete prediction of the future, cannot be realised (although Albert Einstein
(1879-1955) did not agree with Heisenberg, because, according to Einstein, “God does not
play dice with the universe”). According to Heisenberg’s principle, effects do not follow
causes in a rigorous chain of events [Feynman 1965]. Nevertheless, we assume that to a
very good approximation the laws of science behave deterministically. The problem then
becomes one of complexity, there are simply too many variables (or in Laplace’s words,
too many forces and beings that compose nature) to encompass. Because of this, all theories
and models are approximations and we use probabilities to express the resulting
uncertainty 12 . Apparent stochastic behaviour is then introduced in our deterministic view of
the world as a result of our approximations. Each approximation introduces an error term
with respect to the ‘true’ value. The error propagates when numerical operations with other
uncertain quantities are being conducted. Under some conditions the error term may grow
disproportionately fast. Prigogine [1977] introduced the concept of bifurcation points.
According to this theory a system which has bifurcations will imply both deterministic and
probabilistic elements. In between two bifurcation points the system behaves
deterministically, but in the neighbourhood of the bifurcation points fluctuations play an
essential role and determine the ‘branch’ that the system will follow. The outcome of the
model will then be increasingly uncertain when more cause effect relations are called upon,
typically when predictions further into the future are made. Rapid error accumulation may
12
De Finetti (1906-1985) stated that probability is an expression of the observer’s view of
the world and has no existence of its own – probability does not exist (quoted by Lindley
[1986]).
27