76,724 reputation
8126267
bio website quantdec.com
location Northeastern US
age 14
visits member for 3 years, 8 months
seen 15 hours ago

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 I can be reached through (outdated but still valid) links posted on my web site.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


15h
revised Finding an equation with many variables to fit a set of data
edited tags
15h
comment What's so Poisson about a Poisson Point Process? (or, can I generate one using random ordered pairs?)
@adparker "Nothing to do with" seems a little too strong to me. An equivalent formulation of a Poisson point process is that the points are independent and have a uniform distribution over the region. It is called a Poisson process for the reason you give. (PS I edited your comment to make it fit the space available. If any of those changes are objectionable, just flag it for moderator attention and we can fix or delete it.)
16h
comment Finding an equation with many variables to fit a set of data
Because this is such a specific application, specific information beyond "a lot of variables" is needed. Although you don't have to explain them all, it is important to know what kinds of variables they are, how they are measured, what aspects of those measurements you have recorded, and how much data you have. Your edits to the question to clarify these points would be most welcome.
16h
comment Why we shouldn't be obsessed with unbiasedness
I thought you might have that in mind--but then you're in even worse trouble, because you are trying to talk about estimators of something that doesn't even exist! That's not really relevant to the existence (or lack thereof) of biased estimators of actual parameters.
16h
comment Why we shouldn't be obsessed with unbiasedness
For sample sizes of $3$ or greater, the bias of the median does have an expectation and it is zero. The "usual definition" I am using is the difference between the expectation of an estimator and the value of its estimand. (For sample sizes of $5$ or more, it even has a variance. E.g., the variance of the median when $n=5$ is $90\zeta(3)/\pi^4-1/2\approx 0.6106$.)
16h
comment What classification method to use
Thank you for your contribution. Welcome to our site!
16h
comment Why we shouldn't be obsessed with unbiasedness
I believe there are many unbiased estimators of the center of this distribution: the median is one. You might be thinking of unbiased linear estimators.
16h
comment Regresssion of Accurate Data
+1 in light of the clarifications by the O.P. concerning the intent of the question.
16h
comment Can you ever have known parameters?
@rocinante Thanks for replying: in reading over the preceding comments more carefully, I see (and agree with) what you were saying. The population mean is whatever it is; the closing prices on a stock index are a matter of record so there is no statistical uncertainty about their mean, variance, or whatever. Furthermore, because the entire population is available, we do know its distribution, contrary to the assertion in that comment (which led to my potentially confusing comment, for which I apologize).
16h
comment How to properly handle Infs in a statistical function?
It may be worth pointing out that when $x \lt -36$ or so, $1 + \exp(x)$ will evaluate to $1$ (exactly) due to floating point rounding. Similarly, when $x \gt 36$, $1+\exp(x)$ evaluates to $\exp(x)$, whence the quotient produces an exact value of $1$. The precision issues when $|x|\gt 710$ are astronomically smaller!
18h
comment R - How to convert from Mann-Whitney U to Z (or other effect size )?
The sample sizes are the N1 and N2 in the formula for Z. Since you have U, you're all set.
18h
comment Comparing nested, non-linear models
Presumably you will be referring the F-statistic to an F distribution. For that to be valid you need to assume (and verify) the usual assumptions on errors: zero mean, homoscedastic, uncorrelated, etc,--and that they are additive. I bring up this point because it would be natural to take logarithms of both sides of these multiplicative models (which is tantamount to assuming multiplicative error in the original expressions), which would make them not quite so dreadfully nonlinear :-), so it is important to be as explicit about the error structure of your models as possible.
18h
comment Can you ever have known parameters?
Fair enough--but I don't think that's the question being asked here. The interest in this question concerns the extent to which quantities that normally are treated as unknown--the statistical parameters--ever can be considered as "known" by collecting enough data or otherwise. I think the OP's reference to "estimates" makes this interpretation sufficiently clear. You are of course free to respond to a different interpretation--I admit the question is not unambiguous--but I'm suggesting that the direction you are taking is not, in comparison, of as much statistical interest.
19h
comment MC Integration Interval Probability
Your code has a bug: it prints the last random uniform value p in place of the desired value t.
19h
revised MC Integration Interval Probability
added 102 characters in body
19h
comment Can you ever have known parameters?
With a little more Googling I found a reference you might enjoy: Figure 4.1 (p. 58) of Morgan & Henrion's Uncertainty: books.google.com/…. It documents published estimates and confidence intervals for the speed of light from 1870 through 1960. It shows those intervals had less than 40% coverage (and it didn't really improve with more recent experiments).
19h
comment Can you ever have known parameters?
In that application you hypothesize, the speed of light is not a statistical parameter. One has not set out to estimate it but is adopting it as a model assumption. The Google hits that refer to the speed of light as "exact" are misleading, because they define the speed in terms of units of time and distance. One of those, at least, has an uncertainty. This is explained on the physics site. One top Google hit documents the present uncertainty in this estimate at speed-light.info/measure/speed_of_light_history.htm.
19h
comment Can you ever have known parameters?
@rocinante On the contrary: although the mean of a sample always estimates the mean of the distribution, it is not always the best or even a good estimator of the distribution's mean.
19h
comment Regresssion of Accurate Data
If $S$ and $L$ are precisely known then this is a duplicate question asking about regression or response surfaces. The novelty here--if I understand correctly--is that $x$ is the value that is precisely known but $S$ and $L$ are uncertain. This is a case of "inverse regression."
19h
comment MAP Estimator with Laplacian Noise
The issue concerns what is fixed and what varies with each data value. Judging from the code, I am guessing that $x$ is fixed, $\sigma_n$ is fixed, but that $n$ varies independently (and independently of $x$) with each observation of $y$. Is that correct?