Mr. F
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 Mar 22 revised Real analysis question edited body Mar 22 answered Real analysis question Mar 22 comment Finding displacement from origin of SVM hyperplane Scikits.learn, which is a Python layer over LIBSVM, does return the bias parameter within SVM objects. It's easy to use; I would consider it. Mar 22 comment How do you filter through published papers and find the ones you should read? Yeah, like Cross-Validated, Sci-Comp, and Theoretical Computer Science for example. Mar 22 comment Do non-mathematical fields use the appropriate level of analytic/probabilistic rigor? Regarding your comments on probability theory, I think Jaynes wrote the definitive rebuke of dogmatic dependence on measure theory, in Appendix B of his "Probability Theory: The Logic of Science." Reading Jaynes in grad school revived my love of math. Measure theory is important, insofar as it is an expedient tool, and if other folks like it for aesthetic reasons, that's fine. But in general, I think graduate-level education in probability has forgotten that applied math is supposed to be in the service of something... Mar 22 comment P vs NP and Gödel As an interesting aside, Godel wrote a letter to Von Neumann once expressing how, if P=NP, it will be the end of human mathematics, excepting possibly the postulation of axioms. The remark is in this paper (which is well worth a read for most folks here anyway). Mar 22 answered How do you filter through published papers and find the ones you should read? Mar 22 answered Do non-mathematical fields use the appropriate level of analytic/probabilistic rigor? Mar 21 revised Combining independent probabilities of an event added 9 characters in body Mar 21 answered Combining independent probabilities of an event Mar 21 answered Conditional Probability Problem (drawing chips from an urn) Mar 20 comment How to estimate the number of articles on Wikipedia using the “random article” function? This seems like a good problem for a latent random graph model. Given a model of some graph parameters (which will control the number of nodes and the diameter, etc.), you could use some Bayesian model fitting methods to decide which graph likely gives rise to your observed number of pages-before-repeat. That is how I would start, at least. Unlike the German tank problem, this one is sensitive to the graph structure you assume. There are well-confirmed network models of wiki-like graphs, though. Check out M.E.J. Newman's recent book on networks for some examples. Mar 20 comment probability of sequential events Note that it can fail either right away at point 1 (you know the probability of that) or (with probability that it does not fail at point 1) it can fail at point 2 with a probability that you know. Add these to get total probability of failure, F, then 1-F is the probability of success. Mar 20 answered Is it possible to prove that a problem $P$ is decidable in $O(\phi)$ without providing an algorithm that decides $P$ in $O(\phi)$? Mar 20 revised General properties of eigenvalues of a Jacobian matrix when premultiplied by a symmetric, positive definite matrix? added 595 characters in body Mar 20 asked General properties of eigenvalues of a Jacobian matrix when premultiplied by a symmetric, positive definite matrix? Mar 20 revised How to find the conditional expectation for this pdf added 784 characters in body Mar 20 comment How to find the conditional expectation for this pdf You're right. The mistake though is not quite what you mentioned. It is that in my first conditional expectation, I forgot to divide by the marginal probability $P(X_{1} = x_{1})$. Then, multiplying by that again will cancel it to make the last formula correct. I am updating to reflect this. Mar 20 comment How to find the conditional expectation for this pdf But the first term of the product is just for a single value of $x_{1}$. You have to multiply by the probability of that value of $x_{1}$ and sum over all potential choices for $x_{1}$. Mar 20 answered How to find the conditional expectation for this pdf