Neil G
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 Dec 7 awarded Nice Question Oct 31 comment Computing Gradient and Hessian of a vector function @SeeBees: Take a look at Pearlmutter and Schraudolph's work on the R technique that approximates exactly that in linear time. Oct 16 awarded Civic Duty Oct 2 revised Finding $E(X \mid X > Y )$ when $X, Y \sim N(0,1)$ added 7 characters in body Oct 2 answered Finding $E(X \mid X > Y )$ when $X, Y \sim N(0,1)$ Sep 3 comment Intuitive explanation of a definition of the Fisher information Is there a derivative missing in your definition of the score? Aug 30 revised Determinant of Fisher information added 16 characters in body Aug 30 revised Determinant of Fisher information added 16 characters in body Aug 30 answered Determinant of Fisher information Jul 2 awarded Curious Apr 10 comment Beta function derivation @EricAuld: Bayes rule is much easier to think about without the denominator, which is just a constant given your observations. So: $P(q\mid a) \propto P(a\mid q) P(q)$. (These terms are called posterior, likelihood, and prior respectively.) Then, you can fill it in: $\int_0^x f(q \mid a) dq \propto \int_0^x f(q)f(a \mid q)dq \implies f(q \mid a) \propto f(q)f(a \mid q)$. And, the likelihood $f(a \mid q)$ is just $q$ for heads and $1-q$ for tails. Feel free to ask a question on stats.stackexchange. There are a lot of very helpful people there. Apr 9 comment Beta function derivation @EricAuld: Suppose I give you a coin whose bias $p$ you don't know. You flip the coin $n$ times and get heads $a$ times. Then the likelihood induced on $p$ is a Beta distribution. You can work out the Beta distribution up to normalization by writing out the product of the Bernoulli mass function $p^x(1-p)^{1-x}$ for each realization $x_i \in \{0,1\}$ (where $\sum_i x_i = a$ and $\sum_i 1-x_i = n-a$). Apr 2 awarded Tumbleweed Dec 16 awarded Yearling Dec 1 comment What is the purpose of the first test in an inductive proof? IH: All sets of $n \ge 4$ lines on the plane intersect at a single point. If it holds true for $n\ge 4$ points, then it holds true for $n+1$ points since the first $n\ge 3$ points intersect at a point and so too do the last $n$ lines and the two intersection points must be the same point. Therefore, all lines on the plane intersect at a single point. Sep 4 awarded Popular Question Aug 14 comment Reasoning that $\sin2x=2 \sin x \cos x$ +1: This method also gives all of the double-angle (and triple-angle, etc.) formulas. Aug 11 comment An interesting puzzle I think a rough sketch might be that in order to create any significant probability mass in $\vert X-Y \vert$ between 1 and 2, you have to also create mass between 0 and 1. So, $P{|X−Y|≤1}$ is no less than half the LHS? Aug 5 revised Reasoning that $\sin2x=2 \sin x \cos x$ added 116 characters in body Aug 5 answered Reasoning that $\sin2x=2 \sin x \cos x$