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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 I can be reached through (outdated but still valid) links posted on my web site.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.


Dec
27
comment Distribution of the number of children needed so that at least both a girl and a boy are born
Right, but your formula gives a "probability" of $-1$ in the case $k=0$, whereas it should be $0$.
Dec
27
comment Distribution of the number of children needed so that at least both a girl and a boy are born
(1) Take care when $k=0$. (2) What question are you answering? The current one asks for a "distribution" of $N$. (I believe this question needs further clarification in order for the meaning of this request to be properly understood.)
Dec
27
comment Absolute continuity inquality
You may have neglected some additional assumptions: after all, for $u(x)=1$ the rhs is zero while the lhs diverges toward $+\infty$.
Dec
26
comment Why is $\log(\sqrt{x^2+1}+x)$ odd?
It is also crucial that the integral start at $0$ and not someplace else.
Dec
6
comment How to show that the inverse Gaussian density integrates to 1?
One method: look up the CDF (in Wikipedia, say) and differentiate it to prove it is correct. Then evaluate its rightmost limit. Both processes are purely mechanical.
Dec
6
comment How to show that the inverse Gaussian density integrates to 1?
These links seem to address a substantially different question of integrating a Gaussian density rather than the inverse Gaussian.
Nov
30
awarded  Taxonomist
Nov
20
comment is the fixed set of a smooth involution a submanifold?
@Steve It doesn't quite work that way: the z-axis, qua point of the projective plane, also is fixed under this reflection--that's the whole point of the example. To put it another way: an equivalence class (the z-axis) can be fixed without its elements being fixed, so it does not suffice to look only at the fixed points in the covering space. We're not talking about just a single point, either, in general: this example readily generalizes to higher-dimensional projective planes, Grassmannians, flag manifolds, etc., to give a rich set of counterexamples.
Nov
19
comment is it possible to reduce the weight of a best fit line (least squares) given new data points?
Actually, "weight" and "influence" are two completely different things. (See casact.org/pubs/proceed/proceed94/94123.pdf inter alia.) You appear to be looking for the regression version of a time-weighted average. This can be done--as I suggest in an answer to that other question--with a suitable updating algorithm.
Nov
19
comment is it possible to reduce the weight of a best fit line (least squares) given new data points?
A duplicate of this question appeared two years ago at stats.stackexchange.com/questions/6920/… and has some answers there.
Nov
19
comment is it possible to reduce the weight of a best fit line (least squares) given new data points?
@Gerry Actually, if you measure "influence" of a data point as, say, the derivative of the fitted slope with respect to the point's location, then influences vary--a lot. There also is a fairly current and natural definition of "weight" in this context.
Nov
18
comment is the fixed set of a smooth involution a submanifold?
@Steve I don't follow: are you claiming that $(0:0:1)$ lies on the circle of fixed points?
Nov
17
comment is the fixed set of a smooth involution a submanifold?
This argument shows the set is locally a submanifold, but I cannot find a definition of "submanifold" that assures that the entire set will actually be a submanifold: all the definitions I know of are constructed to assure that submanifolds have well-defined dimensions. That's not necessarily the case here.
Nov
17
comment is the fixed set of a smooth involution a submanifold?
The connected components of this subset will each be smooth submanifolds, but their dimensions can vary. As such, their union is not a submanifold. As a simple example, consider the vertical reflection $(x:y:z)\to (x:y:-z)$ of the space of one-dimensional linear subspaces of $\mathbb{R}^3$ (that is, $\mathbb{RP}^2$) to itself, expressed in projective coordinates. It's well-defined and smooth. Its fixed points consist of a codimension-1 submanifold $(\cos(\theta):\sin(\theta):0)$ (a circle of all horizontal lines) together with a codimension-2 submanifold $(0:0:1)$ (the vertical line).
Nov
6
comment The geometric mean of primes less than or equal to $x$
"Amazing"...and truly wrong. Because $e^{x/2}$ exceeds $x$ for all positive $x$, this answer claims that an average of values all of which are less than $x$ actually exceeds $x$! (The source of the error appears to be failure to divide $s(n)$ by $n$ in the linked answer.)
Nov
6
awarded  Custodian
Nov
6
reviewed Reviewed When does a gradient vector of a function not exist?
Nov
6
reviewed Leave Open Show that $f(S)\cup f(T)\subset f(S\cup T)$
Oct
29
comment When does distribution bootstrap mean converge to distribution sample mean?
Cross-posted at stats.stackexchange.com/questions/39297/….
Oct
28
comment Convergence of a sequence
$z \ne 0$ is obvious because it is the limiting value of numbers that lie on the unit circle and $0$ is separated from all those numbers (by a distance of $1$). More rigorously, because $|\exp(itX_n)|=1$ for all $n$ and the norm $||$ is continuous, $|z| = \lim 1 = 1 \ne 0$.