mattmacdermott comments on The Telephone Theorem: Information At A Distance Is Mediated By Deterministic Constraints

mattmacdermott 17 Jan 2023 19:37 UTC
4 points
When you write $P [M_{0} | M_{n}] = P [M_{0} | f_{n} (M_{n})]$ I understand that to mean that $P [M_{0} | M_{n} = m_{n}] = P [M_{0} | f_{n} (M_{n}) = f_{n} (m_{n})]$ for all $m_{n}$ . But when I look up definitions of conditional probability it seems that that notation would usually mean $P [M_{0} | M_{n} = m_{n}] = P [M_{0} | f_{n} (M_{n}) = m_{n}]$ for all $m_{n} .$
Am I confused or are you just using non-standard notation?
- johnswentworth 17 Jan 2023 21:05 UTC
  4 points
  Parent
  Your interpretation of my notation is correct. The notation is not uncommon, but it does diverge from the notation used for conditional probability in other contexts. (More generally, notation for probability is an absolute mess in practice, with context determining a lot.)
  - mattmacdermott 17 Jan 2023 22:40 UTC
    1 point
    Parent
    Thanks. Is there a particular source whose notation yours most aligns with?