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bio website itr.unisa.edu.au/~mckillrg
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visits member for 4 years, 5 months
seen Aug 31 at 8:55

Nov
13
comment Maximum magnitude subset sum
@Gerry My bad, I obviously mean positive integer! Fixed.
Nov
13
comment Maximum magnitude subset sum
@Ricky Thanks, I've made that change.
Jun
13
comment Are Gaussian Processes more important than other stochastic processes?
+1 Couldn't agree more. Sometimes, I think it is a miracle that anything works at all. If I had a dollar for everytime I read, ''Assume that the noise is additive white and Gaussian'', I would be a rich man.
Jun
11
comment Maximum of the norm of k-averages of n iid random d-dimensional vectors
Sounds like you want a 'maximal inequality'. Not exactly sure how to do what you are asking by I would start at Section 3 of stat.yale.edu/~pollard/Papers/Pollard89StatSci.pdf.
Jun
11
comment Hyperplane arrangements and covering numbers
Thanks! I also found Bernard Chazelle's `The discrepency method' to have the same proof on page 206.
Jun
10
comment Hyperplane arrangements and covering numbers
Yes, the hyperplanes are affine.
Oct
29
comment Exponential (or other) families of distributions on manifolds.
I would guess that the answer is `not really'. As far as I know there is not a even a universally accepted definition of the 'normal distribution' on a Remanian Manifold. Probably the closest thing to the normal are those distributions that arise from generalisations of Brownian motion on manifolds. math.northwestern.edu/~ehsu/…
Aug
15
comment Point-wise error estimate in polynomial regression
Sorry, silly typo. Should work just fine for any set of basis functions.
Jul
28
comment More multinomial type integrals over the hypercube
As I said the $x_i^2$ gets in the way. If is was just two multinomials, one to power $k$, the other to power $m$, there would be no problem, you would get $\exp(tx + sx)$ and everything would work out nicely as before. Perhaps I have missed something though. How do you intend to use the integral of $\exp(tx^2 + sx)$ (which has no closed form solution as far as I am aware) taken to the power of $n$ to efficiently compute the answer?
Jul
24
comment A Book You Would Like to Write
How about you just apply Hofstadter's Law: "It always takes longer than you expect, even when you take into account Hofstadter's Law."
Dec
12
comment When is the function of a median closer to the median of the function than the mean of the function is to the function of the mean?
Do you mean to take absolute values? As in $|\mu (f(x)) - f(\mu (x))| > |m (f(x)) - f(m (x))|$?
Dec
6
comment Sequential sampling of Gaussian and von Mises-Fisher Random Variable
I like the updated part of this question +1. I recommend deleting the first part (However, don't do this if you have some specific reason not too). If you don't mind me asking, in what application does this problem occur? Also, what justifies your use of the von Mises Fisher distribution here?
Dec
1
comment Nonlinear circle fit with known radius
There is a big literature on this. Typing 'circle fitting' into google with give you a lot of resources. Most of the approaches I know of deal with estimating both the center and the radius, but they could easily be adapted to estimate just the center if that is what you want. Your question is probably more appropriate for CrossValidated stats.stackexchange.com/questions. You might have better luck there.
Oct
16
comment Estimating direction from a distribution on a circle
Oh yes! I much prefer Herman Wouk's ryhming version ''When in danger or in doubt, run in circles, scream and shout'' anyway. Thanks!
Oct
15
comment Estimating direction from a distribution on a circle
I think, due to the symmetry, it essential does act in a linear way. I'm pretty sure I can describe very accurately how well your estimator will work. I'll post this as an(other) answer a bit later.
Oct
15
comment Estimating direction from a distribution on a circle
I will Will, I will. Just give me a little time.
Oct
15
comment Estimating direction from a distribution on a circle
Actually, I lie. In this case, I think this is exactly what you want to do! I recommend this answer be marked as correct. My answers can just be considered as advertising for the important and interesting the field of circular statistics.
Oct
15
comment Estimating direction from a distribution on a circle
That's a good answer Niels, and I believe it will work quite well in this case. One trouble I see is that by squaring you have multiplied the 'noise' (if you like) by 2. So, I think that this estimator will be consistent, but not efficient.
Oct
14
comment Estimating direction from a distribution on a circle
@Andrei: If you have further questions, feel free to send me an email.
Oct
14
comment Estimating direction from a distribution on a circle
Hi Will, I use metapost. The actually data for the pdf (it's a weighted sum of von Mises distributions by the way) comes from a java library (unfortunately) and then the plotting gets done by metapost. At some point I plan on releasing all of the code I have for simulations and plotting under the CRAPL matt.might.net/articles/crapl. However, at the moment I feel the code is even too crap for the CRAPL :(