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bio website quantdec.com
location Northeastern US
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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 I can be reached through (outdated but still valid) links posted on my web site.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.


Apr
9
comment Probability for a regular matrix
"Isomorphism" in what category? As a linear transformation of $\mathbb{Z}^k$ or as a linear transformation of $\mathbb{C}^k$, perhaps? (The answers differ--a lot.) Or maybe as a linear transformation of $\mathbb{F}_p^k$?
Apr
3
comment Recursive/Fibonacci Induction
This is carried out at mathematica.stackexchange.com/questions/18481/… for Fibonacci numbers defined over any field (whose characteristic is not $5$ or $2$).
Apr
3
comment A question on convex/concave envelope
It is difficult to determine what is being asked here: exactly how is the input going to be specified? Do you need to determine the points where the function ceases to be differentiable or are those points given you? (If they are explicitly given, why not just compute their convex hull?)
Apr
1
comment Fejer Kernel problem
This is really a comment because it's not an answer: although it points out that the integral is invariant with respect to $f'$, it still leaves the O.P. with the problem of finding that constant ("show (1) gives you $1$").
Mar
30
comment Detect values in array that are statistically inconsistent
Option 1 is statistically terrible, for many reasons, and option 2 requires strong assumptions to be valid. Consult the stats site for better solutions and discussion.
Mar
30
comment Detect values in array that are statistically inconsistent
This is not a mathematical question nor does it have a definite answer. For instance, some processes have regular variation when the observations are expressed as logarithms (as is often the case in chemistry: pH is a log). In your first example the common logs all vary between 3.2 and 1.7, averaging around 2. However, one of them is zero: it's far below all the rest. That would make $1$ the outlier, not $1542$. A good answer to this question will therefore consider the nature of the process, its statistical characteristics, and the objectives of the algorithm.
Mar
30
comment Difficult and unusual probability problem, how to solve?
Hint: consider the case $k=1$. What's the answer? (The answer in the general case is obtained in a similar manner and relies on this one.)
Mar
30
comment Find $\lim\limits_{(x,y) \to(0,0)} \frac{xy^2}{ x^2 + y^4} $
+1 Nice reference. For some illustrations, please see mathematica.stackexchange.com/questions/21544/….
Mar
28
awarded  Pundit
Mar
27
comment Hugely ugly messy determinant - any trick to find it?
If you view the determinant as a function of $a$, evidently it's a polynomial of degree $3$. By inspection--and understanding the basic properties of determinants--you can identify three roots immediately, so you know it up to some multiple that depends only on $b$, $c$, and $d$. Repeating this observation for the other variables pins down the determinant up to a constant. By choosing nice values for $a$, $b$, $c$, and $d$, you can compute that constant--and have thereby reduced the problem to finding the determinant of a single matrix with numerical entries.
Mar
19
comment How to find the trigonometric identities?
Did you really mean to post this on a site about Mathematica software? By the way, there is an infinity of trigonometric identities. They can all be determined from a very small number of them in standard ways, such as a statement of the first order linear ODE satisfied by $\cos(x) + i \sin(x)$ (together with their initial conditions) and the definitions of the other trig functions in terms of them, or the power series definition of $\exp(i x)$, or the definition of $\exp(z)$ as the inverse of $\int_1^z \frac{dz}{z}$, or the infinite product representation of $\csc(z)$, etc.
Mar
1
comment A Cover of an Orientable Manifold is Orientable
You used one more thing that you're not explicitly making note of: the existence of a nowhere vanishing form on $M$.
Feb
28
comment Lagrangian Duality Complementary Slackness solution
This isn't really a data analysis question. Math has agreed to look at it. Cheers!
Feb
6
comment Probability proof and combinatorics
I have rolled this question back to its original form because the corrections added in the edit make it incomprehensible: without the typographical errors, there's no question here at all and the comments make no sense.
Feb
6
revised Probability proof and combinatorics
rolled back to a previous revision
Feb
6
comment Probability proof and combinatorics
@Dilip Sorry; I wasn't trying to imply you weren't aware: your comment showed you understood the issues. My comment was intended to help the OP avoid a possible misunderstanding of your comment, which could cause the reader to focus on the second equality in each line without noticing the blatant typographical errors that occurred at the first equality.
Feb
6
comment Probability proof and combinatorics
@Dilip Actually, the $k!$ in the numerator on the first line and the $(n-k+1)!$ on the second line are typos. Upon removing the extraneous "!", all is well.
Feb
5
comment sum of two random variables
+1 There should be no objections from purists: use of $\delta$ can be made rigorous in the (Schwartz) sense of distributions. Integration by parts of the convolution of the PDFs produces an integral which is the product of the derivative of the Gaussian PDF and the Heaviside function, both of which are integrable (even Riemann integrable).
Jan
13
comment Game with losing and winning a dollar
The probability of winning $n$ dollars is $0$ unless $k=0$, because the most that can be won is $n-k$. Perhaps you mean to ask for the probability of reaching a total of $n$ dollars?
Jan
13
reviewed Close What is gained by computing additional digits of $\pi$?