Reasoning under uncertainty #3 - inverse implication

In this clip, an implication will be used the 'wrong way' in order to do probabilistic reasoning. It's assume we know an implication, A implies B and that we then observe B. For example, if it's rain it's overcast and it's overcast now.

It's shown that the probability for the unobserved A (rain) increases when we observe B (overcast).

PS: I may have been switching pictures too swiftly in this clip, so using the pause button can be recommended.

Deductive logic will not get any results here. Claiming so would be the fallacy known as affirming the consequent. Thus a very simple case where probabilistic reasoning gives result where deductive logic does not, is provided.

Category:

Howto & Style

Tags:

• Bayesian
• Bayes
• probability
• probabilistic
• logic
• reasoning
• implication
• implies
• affirming
• consequent

[EverettsVLOG]

My problem with Bayes theorem is that it presupposes induction. I've seen proofs where they simply leave out the use of the Rule of Conditionalization, which is quite odd to me. That is, ORDER OF EVENTS needs to be factored into the calculus by saying:

Pr(n+1)(H) = Pr(n)(H/E)

Otherwise, bayes would not be a predictive formula, it seems to me (you?). But the above rule presupposes induction, as it demands that, future events be judged by past events.

[trondreitan]

You can always look at a model where there is no hope of learning, if you want to. Typically these models will not perform as well as other models, when new data arrives.

[trondreitan]

I'm sorry, but I have problems interpreting you formula Pr(n+1)(H)=Pr(N)(H|E). Is it the idea that the posterior from the previous data forms the prior in the next? if so, that falls out of the probability calculus, as shown in RUU #20.

[ashlah]

fantastic

[jas2754]

Nice examples.... I enjoyed the video a great deal.