#bayes’ theorem

[scientiststhesis-at-pillowfort]

Other ways of looking at probability

Other ways of looking at probability

Bayes’ Theorem is all nice and dandy, but it may not necessarily be the best thing to work with. It’s quite simple:

When laid out this way, what it says is that the probability of some proposition A after you learn that B is true equals its probability before you knew it was true times a factor we could call the impact of B on A. When explaining what the Bayesian meaning of evidence was, I mentioned…

[psycheapuleius]

[usunezukoinezu]

''Suppose the police pull someone over at random at a drunk-driving checkpoint and administer a Breathalyzer test that indicates they are drunk. Further, suppose the test is wrong on average 5 percent of the time, saying that a sober person is drunk. What is the probability that this person is wrongly accused of drunk driving?

Your first inclination might be to say 5 percent. However, you have been given the probability that the test says someone is drunk given they are sober, or P(Test=drunk | Person=sober) = 5 percent. But what you have been asked for is the probability that the person is sober given that the test says they are drunk, or P(Person=sober | Test=drunk). These are not the same probabilities!

What you haven’t considered is how the results depend on the base rate of the percentage of drunk drivers. Consider the scenario where everyone makes the right decision, and no one ever drives drunk. In this case the probability that a person is sober is 100 percent, regardless of what the Breathalyzer test results say. When a probability calculation fails to account for the base rate (like the base rate of drunk drivers), the mistake that is made is called the base rate fallacy.''

-Gabriel Weinberg and Lauren McCann, Super Thinking

[dexlabanalytics]

This blog presents a hands-on understanding of the Bayes’ Theorem. Along with that, we also offer basic understanding of concepts such as Prior odds ratio, Likelihood ratio and Posterior odds ratio.

[scientiststhesis-at-pillowfort]

Logical Uncertainty: an addendum

Logical Uncertainty: an addendum

And I forgot to mention one thing in the last post which is relevant. Gaifman, in his paper, states that if in  we have that then . I’ll quickly show that that’s a theorem of my approach.

Suppose that . In that case, then, my approach has that , because the agent knows B is logically implied by A. If that’s the case, then:

With equality if and only if either (A is logically certain given X) or

[scientiststhesis-at-pillowfort]

Don't be so sure...

Don’t be so sure…

One of the great insights of Bayes’ Theorem is the gradation of belief. This is in fact not how most people intuitively reason! Most people have this intuitive feeling of black-and-white, zero-or-one, believe-or-don’t-believe. When they’re thinking about something they want to believe, they think “Does the available evidence allow me to believe it?” and when they’re thinking about something they