Discussion Overview
The discussion revolves around the concept of conditional independence in probability theory, specifically examining whether conditional independence of two events A1 and A2 given an event B implies their conditional independence given the complement of B. The scope includes theoretical exploration and counterexamples.
Discussion Character
- Exploratory
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant presents a statement to prove or disprove regarding the conditional independence of events A1 and A2 given B and its complement.
- Another participant suggests that there is a counterexample to the statement, referencing a Wikipedia article on conditional independence.
- A subsequent reply requests clarification on the location of the counterexample mentioned.
- Further, a participant provides a specific example involving a probability space with three outcomes and defines events A1, A2, and B to illustrate the point.
- A later reply acknowledges the clarity of the example provided, indicating realization of the counterexample's validity.
Areas of Agreement / Disagreement
Participants do not reach a consensus; there are competing views regarding the implications of conditional independence and the validity of the counterexample presented.
Contextual Notes
The discussion includes assumptions about the definitions of conditional independence and the specific probability space used in the counterexample, which may not be universally applicable.