Talk:Inductive probability

Intention
This is intended as a quick and high level description of inductive probability, highlighting a modern understanding of learning and inductive inference and reasoning.

Thepigdog (talk) 13:30, 1 May 2014 (UTC)

Try again? It reads as a stream-of-conscious list of the author's favorite ideas. Whenever someones mention Occam's Razor, I think "This person doesn't thoroughly understand what he or she is talking about." 208.68.128.90 (talk) 18:22, 3 December 2015 (UTC)

The example given for what Occam's Razor is in conflict with what the wiki page on Occam's razor describes it as. — Preceding unsigned comment added by 38.88.7.50 (talk) 19:33, 15 July 2019 (UTC)

(1) "Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements." (2) "The theory with the shortest encoding in this internal language is most likely to be correct."

How does (2) follow from (1)? It's correct that sentences with short encodings are most likely to be **generated** by the language. This is distinct from whether or not they're likely **to be true**. I can create a language model which gives high probability to empirically false statements. The probabilities assigned to statements seems entirely arbitrary. — Preceding unsigned comment added by 80.5.79.116 (talk) 07:55, 10 September 2022 (UTC)

Note 1
Classical probability is based on events. Probability of outcomes is the same for all observers.

Inductive probability is for statements. Probability depends on the history and prior probability of the observer. The probability is subjective and personal. Two people with similar prior probabilities in similar worlds may end up with divergent probabilities.

It is incorrect to ask "What is the probability of the sun rising tomorrow?". The correct question is "What is your probability of the sun rising tomorrow?". Each person may have a different estimate based on knowledge and experience. A person with no scientific knowledge will base the estimate only on their past history. A scientist may give scientific reasons why the sun will almost certainly rise tomorrow.

So probability is not an absolute property of the world, that all people can agree on. Only when assumptions are made about the world (such as the fairness of coins and dice) does probability become an absolute property of a statement. The statement must then be about the outcome of a series of trials.

All probability is based on the lack of any information that prefers one outcome over another. The world does not need to be fundamentally random for there to be a probability. Only the lack of any information that prefers one outcome over another is needed.

Note 2
A probability is a number representing a personal (or individual) representation of partial information about the truth of a statement. Zero means the statement is false. One means the statement is true. Other values for probabilities are constructed from the principle of indifference. If N mutually exclusive statements exists, for which one statement must be true, and no reason is known to prefer one statement over another, then each statement is given a probability of 1/N.

The principle of indifference
The principle of indifference is the source of many contradictions and paradoxes. Need to address this in the article.

Re-ordering
Possibly needs re-ordering to bring the simpler stuff near the top. Ease the reader into it more. Not sure.

Done.