Reasoning under uncertainty #2b - mathematical foundation

The formulas described in this video will form the core for the rest of the series. However, it should not be necessary to memorize these equations. A web page has been made that lists
the content in this clip:
http://folk.uio.no/trondr/uncertainty/


In this second clip on the mathematical foundations of probability, I the
basic rules for probability calculations. Trhee rules are derived from wanted properties for a measure of plausibility, while three more are derived from the first three. Bayes formula in several forms is then discussed.

A full understanding of the formulas here might not be necessary. hopefully the applied videos will make the concepts here clearer.

A nitpicker's version has been made for thos enot fully satistifed with the basis shown here:
http://www.youtube.com/watch?v=0AVnu-lUosQ

Check out video #4 for a graphical representation of the ideas in this series. For those who find graphics easier than algebraic expressions, it may be illuminating:
http://www.youtube.com/watch?v=va1HfQhrsbg

Category:

Howto & Style

Tags:

• Bayesian
• Bayes
• probability
• probabilistic
• logic
• reasoning
• rationality
• series

[suffering44]

just imagine the world expands, and only the physical things will expand? will it not expand in its diamention of binary things like truth and false plus and minus?

[suffering44]

if we have more than 3 spatial diamentions we might also have other diamntions the trick is to discover and invent them

[suffering44]

well yeah thats the current definition in set theory. I didnt like that because it didnt sound very beautiful to me but it is simple and far more usefl and efficient. And more over I thought that even though we can select one apple out of two apples, and divide in to two sets, selected apple and unselected apples we cannot nessasaryly have it as a universal law to use in mathematics. but it was my thought that we must always have something that doesnt follow a certain law in real world.

[trondreitan]

I'm not sure if I understand you correctly. it is so that for any element, e, it has to be either in a set A or it's complement. That's per definition of the complement. And if you have a set A, then the only other set you can construct using only A is the complement. That doesn't mean that you can't operate with other sets as well, though. Set's that may contain some elements both in A and in the complement of A. But this discussing has more to do with clip 2a than this clip, I think.

[suffering44]

why do we only have defined complement and the set and not anything other than it? so e have only A and notA. I have long things to say about that but I know you are busy.

[suffering44]

well I thought we cannot talk of truth and god living in side our language of reasoning.

I thought that trying to explain what truth is using the rules of truth underlining our mind is not valid. But it has nothing to do with your video I only said that because they started to talk about it. And truth according to me has to be replaced by "rigorous beauty"

[VeritasEtLibertas82]

This is awesome.

Thanks.

[shintopunk]

Don't worry, I know what you're saying, I give in. Thanks for the chat.

[shintopunk]

Plus, surely, if I believed God would love me if I killed my mother and he believed god wouldn't love me if I killed my mother, the probabilities would be redundant because we would both have reached certainty, albeit on different sides of the coin, I suppose leaving the jury in a certain state of uncertainty.

[trondreitan]

If the probabilities are unequal then either the models are different or the priors (the belief) are different. If I were you, I would then communicate with your brother and find where your models+beliefs differ.