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 Nov21 comment What algorithm is used by computers to calculate logarithms? @Aryabhata: Thank you for the updated links. I'm looking forward to reading the material. Nov17 comment What algorithm is used by computers to calculate logarithms? @Aryabhata: If I google "What algorithm is used by computers to calculate logarithms", then the first answer shown is this StackExchange webpage, and the first answer is yours with the broken links. That is not very useful. Nov15 comment What algorithm is used by computers to calculate logarithms? @Aryabhata: The links in your post are no longer active. Regarding your statement "this pdf you can find by a google search of the title," what title are you referring to? I would like to search for whatever that is. Oct17 accepted Probability of server cluster failure Oct14 awarded Supporter Oct14 comment Probability of server cluster failure Thank you. Now that I look further, I find it kind of extraordinary that $Pr$(0 servers fail) = $0.00592$. That seems really low when each of the servers seems pretty stable with each having probability $0.95$ of failing. But the math proves it, I guess. Oct14 comment Probability of server cluster failure Thanks. So when I was earlier computing that $Pr$(2 server fails) = $0.95^{98}×0.05^2$, does that imply that I was computing the probability that the first 98 servers were good and the last 2 servers failed? Oct14 asked Probability of server cluster failure Aug21 awarded Nice Question Jul2 awarded Curious Nov16 asked How do I state a reduction in cost? Sep18 awarded Commentator Sep18 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? Sep17 revised Convex hull questions added 1162 characters in body Sep17 asked Convex hull questions Sep15 awarded Notable Question Sep2 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? Sep2 accepted Why would I use Bayes' Theorem if I can directly compute the posterior probability? Sep1 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? Aug26 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?