Mike Wierzbicki
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 Feb 5 comment How to prove the number of solutions to nine dots puzzle I am just now really diving into your solution as your images don't load correctly on my work computer. Great work and nice write-up! Nov 12 comment Could someone explain conditional independence? @zenna What if B works and lives in the same building? Mar 6 comment Rigorous book on bootstrapping, boosting, bagging, etc. @user782220 Upon more searching, I would surmise that Peter Hall's bootstrap book is probably the most rigorous one out there. Mar 6 comment Rigorous book on bootstrapping, boosting, bagging, etc. @user782220 If you're still not satisfied, the Stats SE has a good number of machine learning folks who may offer a different perspective. Mar 6 comment Rigorous book on bootstrapping, boosting, bagging, etc. @user782220 For the boosting list, I'd start with the 'overview' papers he lists. Schapire's papers seem to be on the more rigorous end of the spectrum. For bagging, Breiman's papers are the place to start. Also, the bagging list has a few Annals of Statistics papers. These are (obviously) from a statistical point of view, but are quite 'rigorous.' As for Efron's books, I don't know how 'rigorous' you're hoping to get, but you really can't go wrong with the 1994 text (IMO). Another good bootstrap reference is Davison & Hinkley. Feb 19 comment How to get from $a\sqrt{1 + \frac{b^2}{a^2}}$ to $\sqrt{a^2 + b^2}$ Hint: for positive $a$, $a = \sqrt{a^2}$. Feb 6 comment Time Series and statistics @Probabilityman Oops, sorry about that. Feb 6 comment Time Series and statistics @DilipSarwate Ah sorry, yes I think you're correct. It was previously written as (Xt - j) and I didn't even think about whether it should be X(t)-j or X(t-j). The latter makes much more sense. Jan 18 comment Mathematical toys? Define "serious." Jan 16 comment Generalization of variance to random vectors Note: the covariance matrix contains covariances, not correlations (i.e. the elements are not constrained to $[-1,1]$). Further note: the diagonals of the covariance matrix are variances. Nov 4 comment Finding a formula to sum natural numbers up to $n$ I love this trick -- usually blows the mind of at least one student when shown to them. Can you do something similar for the sum of squares, cubes, etc? Nov 4 comment Working out the variance of the Poisson distribution Take a look at factorial moments and factorial moment generating functions (That's what he's using). Nov 2 comment Expressing the Venn diagram Also be careful with what you're taking out when you add $(E-C)$. Nov 2 comment Expressing the Venn diagram $(A\cap B\cap C)$ is counted in $(A\cap B) + (A\cap C)$ twice, so if you subtract $(A\cap B\cap C)$, you're still left with one. Oct 27 comment Are there any (pairs of) simple distributions that give rise to a power law ratio? +1 Nicely done. I didn't bother with fact-checking as my answer was meant more of a 'point-in-the-right-direction' rather than a 'here's-the-solution.' More wise advice from Dilip: fact-check your sources. Oct 24 comment What is the following Calculation about? Hi testiii, I converted your math to LaTeX. Can you make sure I copied the problem correctly? Oct 22 comment Stuck trying to prove an inequality @Phira I get $9\leq 2+0+2+2+0+2+2+0+0=10$. Oct 22 comment Are there any (pairs of) simple distributions that give rise to a power law ratio? Wise advice. Always check what notation is being used. Oct 21 comment What is the relationship of $\mathcal{L}_1$ (total variation) distance to hypothesis testing? @cardinal I believe you're right. There's another subtle step hidden: $TV(P_0, P_1)=\sup_A (|P_0 - P_1|)$, so you need to convince your self that $\sup_A (|P_0 - P_1|)=\sup_A (P_0 - P_1)$ (which doesn't take much convincing). Oct 20 comment Expected number of draws until the first good element is chosen @MikeSpivey +1 Of course! Serves me right for thinking through the problem too quickly! I'll remove it to avoid confusion.