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Are there any branches of mathematics where causality is incorporated? For example, in Bayesian probability:

$$ \ P(B|A) = \dfrac{P(A ∩ B)}{P(A)} \ $$

likewise:

$$ \ P(B|A) = \dfrac{P(A | B)P(B)}{P(A)} \ $$

there doesn't seem to be a notion of time or causality since A could happen before B or vice versa.

Is there a way to determine that B is a necessary but not sufficient event for A to happen, for example? For example, the probability that B happens given A is zero B happens before A, but some other value if A happens first?

Alexander Mills
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    Check out Judea Pearl's notion of a causal network: https://www.google.com/search?q=pearl+causal+networks – Qiaochu Yuan Sep 17 '22 at 22:29
  • See my answer on CrossValidated: https://stats.stackexchange.com/questions/568281/is-there-any-theory-or-field-of-study-that-concerns-itself-with-modeling-causati/568294#568294. – Adrian Keister Oct 12 '22 at 15:44

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There is, in fact it is called "Causality"

There absolutely is a branch of Math/Stats/CS dealing with precisely such a statistical notion of causality. Most people in the field would simply refer to it as "Causality". The Book of Why gives a good introduction to the main ideas, and the Elements of Causal Inference presents the foundations and a broader view of the field. For a more comprehensive treatment of structural causal models, have a look at the book Causality.

Literature in the field can be found in dedicated venues such as the Journal of Causal Inference or the Conference on Causal Learning and Reasoning, but is perhaps most often published in broader venues in Statistics and, more recently but very notably, machine learning.

Scriddie
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