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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
Mar
26
asked “Tessellate” $e^{-x}$
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$
May
7
awarded  Caucus
Apr
15
comment Log likelihood of a realization of a Poisson process?
Hi David, do you have a citation for the likelihood? I arrived at the same likelihood by reason directly from the entropy of a Poisson process given by McFadden.
Apr
14
awarded  Notable Question
Mar
21
accepted Graphically, what is positive semidefinite-ness?
Mar
21
comment Graphically, what is positive semidefinite-ness?
Thanks, I think I see it now. Essentially, Newton's method is looking for points with zero slope, and decides for each eigenvector whether to go towards a local maximum or minimum based on the sign of the eigenvalue. Is that right?
Mar
21
comment Graphically, what is positive semidefinite-ness?
Thanks for taking the time to answer. You're right that Newton's method will only give a local minimum (and will stop at a local maximum) since it's looking for a point where the gradient is zero. I am still having trouble visualizing the second part of your answer.
Mar
20
revised Graphically, what is positive semidefinite-ness?
added 282 characters in body
Mar
20
revised Graphically, what is positive semidefinite-ness?
obvious