Cosmic acceleration rediscovered

"g" == greywolf42 writes:

g Joseph Lazio wrote in message
g ...

A basic aspect of signal processing is dealing with and
extracting signals from data streams for which the
signal-to-noise ratio is less than unity.

g That's if you know that you have a signal. Because you sent one.

I suspect that there are lots of people (not astronomers) who
spend time processing data streams to see if signals are present.
Indeed, I suspect that the entire field of signal processing would
be a lot more boring if one could only process data streams for
which one knows a signal to be present.

g Your suspicions are both unfounded and irrelevant.

I leave it to the reader to determine whether s/he can imagine anybody
who might be interested in processing data streams to see if signals
are present.

[...]
Indeed, a simple example is estimating the mean and uncertainty
in the mean from a set of data.

g Yes. And a sample of random noise *will* give you a mean and an
g uncertainty in the mean. It doesn't mean that you have a real
g signal.

You don't specify the kind of random noise to which you're
referring, but, yes, random noise can have a mean. Perhaps the
most basic is the normal distribution, which is specified
completely by its mean and variance.

So? Without a better specified problem, your objection is somewhat
meaningless.

g But I specified the problem. The signals claimed are below the
g physical resolution of the detector.

Greg H. has disputed that point, at least as it refers to COBE.

[...]
Conversely, if I estimate the mean and its uncertainty, find that
it is not consistent with zero, and conclude that there is a
signal, what have I done wrong?

g That would depend upon how you "found" that the mean and
g uncertainty were not "consistent with zero." If -- as in the case
g under discussion -- you were claiming a result below the resolution
g of the detector -- then you would be wrong.

Yes, when you start trying to nitpick my statements like this, it
leads me to believe that you don't understand what I'm describing.
This is Data Analysis 101. Let your detector be anything you want it
to be. Let it measure temperature on the sky, volts out of a
voltmeter, whatever. If you take a long data stream from it, you can
easily measure well below the "resolution" of the detector.



More generally, of course, knowing the uncertainties in the
individual data is one of the great challenges in experimental and
observational sciences.

g That phrase indicates that someone is challenged in this arena, all
g right. First, I think you mean "individual datum". Data is
g plural.

Yes, datum is made plural in a manner like that of a second declension
Latin noun, IIRC. However, in English, terms should agree in number.
As I wrote "uncertainties," the modifying prepositional phrase must
agree in number. Is the grammar lesson over yet?


g And an individual datum has no statistical uncertainty. Groups
g of measurements of a single parameter (i.e. data) have a resulting
g statistical uncertainty.

Yes, but why are you restricting just to "statistical uncertainty"? I
made the more general statement that knowing (estimating would have
probably been better) the uncertainties is challenging. There
certainly can be a statistical uncertainty associated with
measurements, but there can be other kinds, too.

(Oh, yeah, I was also taught not to begin a sentence with a conjunction.)

There are ways to estimate the uncertainties (for instance,
calculating the standard deviation of the data),

g That is the *only* way to get statistical uncertainty.

What if there's some systematic effect? What if the process is not
well described by a gaussian random noise process, in which case the
common method of calculating the standard deviation doesn't produce a
meaningful measurement of the variance of the underlying distribution?

--
Lt. Lazio, HTML police | e-mail:
No means no, stop rape. | http://patriot.net/%7Ejlazio/
sci.astro FAQ at http://sciastro.astronomy.net/sci.astro.html

Joseph Lazio wrote in message
...
"g" == greywolf42 writes:

g Joseph Lazio wrote in message
g ...

A basic aspect of signal processing is dealing with and
extracting signals from data streams for which the
signal-to-noise ratio is less than unity.

g That's if you know that you have a signal. Because you sent one.

I suspect that there are lots of people (not astronomers) who
spend time processing data streams to see if signals are present.
Indeed, I suspect that the entire field of signal processing would
be a lot more boring if one could only process data streams for
which one knows a signal to be present.

g Your suspicions are both unfounded and irrelevant.

I leave it to the reader to determine whether s/he can imagine anybody
who might be interested in processing data streams to see if signals
are present.

Non-sequiteur combined with the special plead.

[...]

Indeed, a simple example is estimating the mean and uncertainty
in the mean from a set of data.

g Yes. And a sample of random noise *will* give you a mean and an
g uncertainty in the mean. It doesn't mean that you have a real
g signal.

You don't specify the kind of random noise to which you're
referring, but, yes, random noise can have a mean. Perhaps the
most basic is the normal distribution, which is specified
completely by its mean and variance.

So? Without a better specified problem, your objection is somewhat
meaningless.

g But I specified the problem. The signals claimed are below the
g physical resolution of the detector.

Greg H. has disputed that point, at least as it refers to COBE.

Greg H is free to dispute that point. But I will no longer respond to him
on this thread, due to repeated bold-faced lies on his part, within the
thread. If you feel that he has a point, (and a reference to back it up)
feel free to take up the position.

[...]

Conversely, if I estimate the mean and its uncertainty, find that
it is not consistent with zero, and conclude that there is a
signal, what have I done wrong?

g That would depend upon how you "found" that the mean and
g uncertainty were not "consistent with zero." If -- as in the case
g under discussion -- you were claiming a result below the resolution
g of the detector -- then you would be wrong.

Yes, when you start trying to nitpick my statements like this, it
leads me to believe that you don't understand what I'm describing.

LOL! Look, you simply *asserted* that you had "found" that the mean and
uncertainty were not consistent with zero. This is simply
proof-by-assertion.

This is Data Analysis 101. Let your detector be anything you want it
to be. Let it measure temperature on the sky, volts out of a
voltmeter, whatever. If you take a long data stream from it, you can
easily measure well below the "resolution" of the detector.

LOL! Another proof-by-assertion. Citation, please.

Tom Roberts calls this "overaveraging" the results. And he gets livid when
Miller did this at less than 1 order of magnitude below his data. Yet he
has no problem accepting such results as much as 4 orders of magnitude below
resolution -- if the claimed results match his prejudices.

More generally, of course, knowing the uncertainties in the
individual data is one of the great challenges in experimental and
observational sciences.

g That phrase indicates that someone is challenged in this arena, all
g right. First, I think you mean "individual datum". Data is
g plural.

Yes, datum is made plural in a manner like that of a second declension
Latin noun, IIRC. However, in English, terms should agree in number.

LOL!

As I wrote "uncertainties," the modifying prepositional phrase must
agree in number. Is the grammar lesson over yet?

Apparently, I need to start one for you.

g And an individual datum has no statistical uncertainty. Groups
g of measurements of a single parameter (i.e. data) have a resulting
g statistical uncertainty.

Yes, but why are you restricting just to "statistical uncertainty"?

Because that is the only uncertainty that exists in experimental science.
Accuracy and precision are different terms.

I
made the more general statement that knowing (estimating would have
probably been better) the uncertainties is challenging. There
certainly can be a statistical uncertainty associated with
measurements, but there can be other kinds, too.

Not in experimental science.

(Oh, yeah, I was also taught not to begin a sentence with a conjunction.)

And me too. It doesn't matter to the physics, unless the meaning is lost.
(As it was in your statement about the plural of data and the uncertainties
in an "individual data."

There are ways to estimate the uncertainties (for instance,
calculating the standard deviation of the data),

g That is the *only* way to get statistical uncertainty.

What if there's some systematic effect?

Then you get a systematic error -- not an uncertainty.

What if the process is not
well described by a gaussian random noise process,

That is a repeat of the question on systematic effect.

in which case the
common method of calculating the standard deviation doesn't produce a
meaningful measurement of the variance of the underlying distribution?

Sure it does. Please learn the distinction between the terms accuracy,
precision and uncertainty.

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

In article ,
greywolf42 wrote:
Greg H. has disputed that point, at least as it refers to COBE.

Greg H is free to dispute that point. But I will no longer respond to him
on this thread, due to repeated bold-faced lies on his part, within the
thread.

I have not lied in this thread, or in any other thread. You
misunderstood my arguement, and falsely accused me of lieing. Now you
seem to have a pet excuse for not replying to my comments.

Greg Hennessy wrote:
In article ,
greywolf42 wrote:

Greg H. has disputed that point, at least as it refers to COBE.

Greg H is free to dispute that point. But I will no longer respond to him
on this thread, due to repeated bold-faced lies on his part, within the
thread.


I have not lied in this thread, or in any other thread. You
misunderstood my arguement, and falsely accused me of lieing. Now you
seem to have a pet excuse for not replying to my comments.

Yes, that's his standard modus operandi...

Strange that he has not called you a troll so far. ;-)


Bye,
Bjoern