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bio website quantdec.com
location Northeastern US
age 14
visits member for 3 years, 11 months
seen Jul 21 at 13:07

Consultant (environmental and spatial stats a specialty), expert witness, and teacher. I can be reached through (outdated but still valid) links posted on my web site.

Twitter: @WilliamAHuber // ASA-P website: http://amstatphilly.org/


Why waste time learning, when ignorance is instantaneous?

--T(iger) Hobbes.

For any complex problem there is a simple solution. And it's always wrong.

--[Mis?]attributed to H.L. Mencken by Dava Sobel, Longitude.


Jul
5
comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.
You have hit on the crux of the matter: the question, to be unambiguous, must somehow include enough information to enable calculation of all probabilities. In some settings those probabilities are given explicitly, but usually some particular process whereby the randomization is achieved is described. When the process consists of placing each blue ball within one of the spaces between red balls, all with equal probability (of $1/15$), and doing so in a way that the placement of one blue ball affects no other blue balls, you get the multinomial probabilities.
Jul
5
comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.
Perhaps an illustration would help. In the case $n=k=2$ there are two distinguishable configurations modulo symmetries of the circle: RBRB (red-blue-red-blue in counterclockwise order) and RBBR. In the multinomial scenario both are assumed to have probability $1/2$, while in the permutation scenario they are assumed to have probabilities $1/3$ and $2/3$, respectively. Some people have argued that absent any additional information, one should assume the maximum-entropy distribution. That's the multinomial one in this case--not the permutation one!
Jul
5
comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.
Yes I can still come up with two (and even more) solutions. In this post I have explained two ways of looking at the situation that are perfectly consistent with the problem. If you disagree, the burden is on you to demonstrate how one (or even both!) violate some explicitly-stated criterion in the problem statement. I would even go so far as to accept that there are some conventional implicit criteria in questions like this one: the obvious one is that the distribution ought to be invariant under symmetries of the configuration. That is the case in both scenarios.
Jul
5
comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.
No, that's not right. "Random" is not a quantitative characterization: you have to specify the process involved. The problem statement does not give enough information to "assess" a unique distribution. Both my answers are correct given their assumptions about how the balls are distributed randomly. One of them happens to agree with yours, but that only means it likely adopted the same assumptions you did.
Jul
1
comment How to understand Demartines theorem
This is a minor variant of the Central Limit Theorem, which asserts the standardized version of $||X||_2^2$ is asymptotically Normal. It requires that $X$ have finite variance.
Jun
26
comment Transforming vector elements to element indices
Because matrix operations represent linear transformations and the relationship between Y and X is not linear, no such Q exists.
Apr
7
comment Holder's inequality
Your second statement is not well defined until you assume both $X$ and $Y$ are strictly positive.
Feb
26
comment Lower bound for non-negative definite matrix
The matrix $$\left( \begin{array}{cc} 0 & 1 \\ -1 & 2 \\ \end{array} \right)$$ is non-negative definite but your expression equals $-2$. Perhaps you would like to stipulate that $A$ also be symmetric?
Dec
16
comment Determine the number of revolutions the normal to a curve makes as it moves along a curve in three dimensions?
That is correct, which is why I claimed your question is not well-defined! It only becomes so once you fix a pair of points on the sphere once and for all.
Dec
6
comment If $X$ is independent of $Z$ and $Y$ is dependent with $Z$ is it possible for $X + Y$ to be independent of $Z$?
@Did Thank you for pointing that out!
Dec
6
comment If $X$ is independent of $Z$ and $Y$ is dependent with $Z$ is it possible for $X + Y$ to be independent of $Z$?
If $X+Y$ is independent of $Z$ and $X$ is independent of $Z$, then $(X+Y)-X = Y$ must also be independent of $Z$.
Dec
6
comment Determine the number of revolutions the normal to a curve makes as it moves along a curve in three dimensions?
You can make this question well-defined by first restricting to curves whose normals are never zero, allowing you to define a unit normal everywhere, and assuming this unit normal is a continuous map into the unit sphere. Select two points on the unit sphere not in the image of that map. Use (say) a stereographic projection based at one of them to project the curve into the plane. Define the number of "revolutions" to be the winding number of the (projected) unit normal around the second point.
Dec
6
comment Mapping CDF's to each other
The result is false for discrete distributions. A simple example is given by two Bernoulli variables with parameters $p$ and $p'$ such that $p\ne p'$ and $p\ne 1-p'$.
Oct
25
comment How do you calculate an upper-confidence bound on a problem with 2 means?
That's right--and leave out the left endpoint of the interval altogether.
Oct
25
comment How do you calculate an upper-confidence bound on a problem with 2 means?
This is a nice exposition but it addresses a slightly different problem: the question asks for a UCL of the mean, not a symmetric CI for the mean.
Oct
24
comment Bound of Standard Normal Integral
The upper bound given by $1/\sqrt{2\pi}$ for $-1\lt z\lt 1$ and $(1/\sqrt{2\pi})|z|\exp(-z^2/2)$ otherwise is easy to integrate explicitly.
Oct
15
comment Prove that a polygon with nonnegative area is determined by at least three points.
@Sawarnik I wasn't claiming the question concerns anything other than Euclidean geometry. Pointing out that this statement is wrong in other geometries demonstrates the logical necessity of invoking some axiom that is enjoyed by Euclidean geometry.
Aug
30
comment Name for this matrix operation?
Because there are many ways to describe this operation (outer products, tensor products, etc), and it's really about a purely mathematical question, I think the math community may (a) have more interest in it and (b) be able to provide a broad and insightful collection of useful answers.
Jun
19
comment Bottom to top explanation of the Mahanalobis distance?
Cross-posted at stats.stackexchange.com/questions/62092/….
May
14
comment Prove that a polygon with nonnegative area is determined by at least three points.
But there's still something to show, because there exist two-point polygons on the sphere having nonzero area.