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awarded  Nice Question
Jul
2
awarded  Curious
Nov
16
asked How do I state a reduction in cost?
Sep
18
awarded  Commentator
Sep
18
comment Convex hull questions
Thanks. Can you point me to any resources on how to create a line or hyperplane through the "B" point that does not pass through any "A" point?
Sep
17
revised Convex hull questions
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Sep
17
asked Convex hull questions
Sep
15
awarded  Notable Question
Sep
2
comment Why would I use Bayes' Theorem if I can directly compute the posterior probability?
Regarding (3) and my example with 10 years of data, would it be ok to compute a prior probability for $P(team\ wins)$ directly from the winning percentage over 9 seasons, and then use the data from the 10th season to compute the likelihood $P(team\ scores\ 100 | team\ wins)$ and evidence $P(team\ scores\ 100)$, with the resulting posterior probability distribution being used to predict games in the future (after the 10th season is over)? Why not just use all 10 seasons to compute the prior, likelihood, and evidence?
Sep
2
accepted Why would I use Bayes' Theorem if I can directly compute the posterior probability?
Sep
1
comment Why would I use Bayes' Theorem if I can directly compute the posterior probability?
Thanks for the detailed answer. Follow-up questions: (1) If I compute $P(team\ wins | team\ scores\ 100)$ directly as I suggested, would it be correctly called a 'conditional probability' rather than a 'posterior probability'? (2) Is the prior probability the ONLY difference between a frequentist's conditional probability and a Bayesian's posterior probability? That is, the Bayesian pulls the prior out of somewhere, but not from the sample? (3) Where would I get the prior if not from the sample? Would I compute it from 10 seasons of NBA games rather than a sample of one season?
Aug
26
comment Why would I use Bayes' Theorem if I can directly compute the posterior probability?
Can you explain the difference between probability and density? By "density", do you mean "distribution", like a Gaussian distribution? By the way, I'm a software programmer, not a mathematician. Also, how can you safely say that "You don't know $f(\theta|x)$ generally, but you know $f(x|\theta)$ ..."? In my example with the logs of all NBA games, I would be able to compute $f(\theta|x)$, right?
Aug
25
awarded  Promoter
Aug
24
awarded  Tumbleweed
Aug
20
accepted Bayes Theorem with joint probability evidence?
Aug
19
asked How do I state that a data set has a 'denser' standard deviation?
Aug
19
comment Bayes Theorem with joint probability evidence?
Thanks for the answer. I was looking for a webpage that showed a right-hand-side with joint probability evidence but couldn't find one. Now, about going beyond the formula, I was reading about Naive Bayes classifiers, and I think you can simplify Pr(A & B | Z) to be Pr(A | Z) x Pr(B | Z) by the chain rule of probability and assuming conditional independence.
Aug
19
asked Bayes Theorem with joint probability evidence?
Aug
17
revised Why would I use Bayes' Theorem if I can directly compute the posterior probability?
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Aug
17
asked Why would I use Bayes' Theorem if I can directly compute the posterior probability?