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Thread: Uncertainty

  1. #1
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    Uncertainty

    I am posting "definitely" extrasolar fireballs in the Astronomy section. Are they really certain?
    When an eccentricity (or any scientific date) is given as 1.968 +/- 0.355 does that mean it cannot be less than 1.613 or does it mean there is a one in quintillion chance (say) that it is as low as 0.999?
    I tried looking on Google but can't get an answer to this I understand and don't remember from my 41 year old B.S. education.
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    It'll be a confidence interval of some sort (which is to say, there will be a quantified probability that the true value lies outside the quoted +/- range). You need to look at the documentation to find out what it means, because different authors mean different things.

    Grant Hutchison

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    Quote Originally Posted by Tom Mazanec View Post
    I am posting "definitely" extrasolar fireballs in the Astronomy section. Are they really certain?
    When an eccentricity (or any scientific date) is given as 1.968 +/- 0.355 does that mean it cannot be less than 1.613 or does it mean there is a one in quintillion chance (say) that it is as low as 0.999?
    I tried looking on Google but can't get an answer to this I understand and don't remember from my 41 year old B.S. education.
    The quoted uncertainty in a measurement is always an estimate, and always represents a confidence interval where there's some (high) percentage likelihood that the true value is in that range. There is always a chance that the true value could be outside that range, although as you suggest in this case, the true value being three times as far away from the stated value is extremely unlikely.
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    Quote Originally Posted by grant hutchison View Post
    It'll be a confidence interval of some sort (which is to say, there will be a quantified probability that the true value lies outside the quoted +/- range). You need to look at the documentation to find out what it means, because different authors mean different things.

    Grant Hutchison
    Very frequently the +/- value is one, two, or three standard deviations, which for a normal distribution would include 68%, 95%, or 99.7% of the data, but as Grant says, you'd have to look at the reference to know if that is what they are reporting, and if it is a normal distribution.

    And yes, even if those values are three standard deviations, and it is a normal distribution, there is a chance that the value could be outside those limits.
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    Quote Originally Posted by Swift View Post
    Very frequently the +/- value is one, two, or three standard deviations, which for a normal distribution would include 68%, 95%, or 99.7% of the data, but as Grant says, you'd have to look at the reference to know if that is what they are reporting, and if it is a normal distribution.

    And yes, even if those values are three standard deviations, and it is a normal distribution, there is a chance that the value could be outside those limits.
    Well, I give the actual values, so you can judge for yourself. I donít know about the exact number of standard deviations or the distribution however. I will try asking the manager of the site.
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    Eccentricity is not alway normally distributed (it depends on what orbits you're sampling), and I have to say that the numbers Tom has been posting scream "not normally distributed" to me, but that may be because Tom is sampling the tail of a sample.

    Grant HUtchison

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    Well, I got my answer.

    The uncertainties are huge, due to geometries, errors in tracking, etc., etc. There are no hyperbolics/interstellars in the dataset – when we check the suspect events with manual reductions, everything is bound in the Solar System within the uncertainties.
    See attached paper
    Regards,
    William J. Cooke
    Lead, NASA Meteoroid Environments Office
    EV44
    Marshall Space Flight Center, AL 35812

    I guess that's the end of my posting...no point if they are not interstellar.
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    Quote Originally Posted by Tom Mazanec View Post
    I am posting "definitely" extrasolar fireballs in the Astronomy section. Are they really certain?
    When an eccentricity (or any scientific date) is given as 1.968 +/- 0.355 does that mean it cannot be less than 1.613 or does it mean there is a one in quintillion chance (say) that it is as low as 0.999?
    I tried looking on Google but can't get an answer to this I understand and don't remember from my 41 year old B.S. education.
    It could be a non-standard uncertainty evaluation, because you are supposed to round uncertainties to two significant digits at most.

    The probability is almost certainly a lot higher than one in a quintillion that the true value lies outside the limits. As others have said, commonly this would be 32% or 5% chance depending on the coverage factor.

    Sometimes scientific literature states the standard uncertainty, which means only 68% probability of the true value being in the range. But when they do this, they usually give it in brackets rather than +/-, e.g 1.23(12) means the standard uncertainty is 12 in the last two digits of the value, i.e 0.12.

    If they are proper scientists they should give a statement indicating what their uncertainties actually mean, in particular they should give the coverage factor.

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    Quote Originally Posted by Tom Mazanec View Post
    Well, I got my answer.

    The uncertainties are huge, due to geometries, errors in tracking, etc., etc. There are no hyperbolics/interstellars in the dataset – when we check the suspect events with manual reductions, everything is bound in the Solar System within the uncertainties.
    See attached paper
    Regards,
    William J. Cooke
    Lead, NASA Meteoroid Environments Office
    EV44
    Marshall Space Flight Center, AL 35812

    I guess that's the end of my posting...no point if they are not interstellar.
    Can you give details of the "attached paper"? That would potentially be the most interesting thing about this episode.

    Grant Hutchison

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    It is a little beyond my rusty level of expertise. Since this was about (nonexistent) hyperbolic orbits, here is what they have on that:

    2.3 Trajectory and orbit analyses
    Correlated events – those that are detected by at
    least two cameras and have passed either ASGARD’s fil-
    ters or visual inspection – are automatically analyzed
    on the server. The atmospheric trajectory is determined
    using the program MILIG (Borovicka, 1990); a full de-
    scription of the “straight least-squares method” can be
    found in that paper. The geocentric meteor position as
    a function of time in rectangular and WGS84 coordi-
    nates, the apparent meteor radiant in geocentric rect-
    angular and equatorial coordinates, the convergence an-
    gles, the topocentric azimuth and zenith distance, and
    the average atmospheric meteor speed are calculated
    and output by MILIG.
    The heliocentric orbit is calculated using the pro-
    gram MORB (part of the program FIRBAL; Ceplecha,
    1987). The average observed velocity is corrected for
    Earth’s rotation and gravity. The meteor radiant is
    also corrected and transformed to J2000 geocentric ra-
    diant coordinates. The heliocentric velocity and ecliptic
    latitude and longitude are calculated using the geocen-
    tric velocity and radiant position. The J2000 orbital
    elements follow from these quantities.
    The data pipeline and analysis are automated and
    meteor results are stored in a database; the most re-
    cent three weeks of data are available through a public
    websitea.

    The paper is WGN, the Journal of the IMO 48:3 (2020) pages 60 to 68.
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  11. #11
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    Thanks, but in the this context title and author would be useful, which might make it possible to hunt down a copy sitting on a server other than the IMO's. (The journal is a members-only pdf). The most likely route to access is arxiv or an author's personal webpage, but a search on key phrases from the text you quote turns up nothing.

    Grant Hutchison

  12. #12
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    Quote Originally Posted by Tom Mazanec View Post
    It is a little beyond my rusty level of expertise. Since this was about (nonexistent) hyperbolic orbits, here is what they have on that:

    2.3 Trajectory and orbit analyses
    Correlated events – those that are detected by at
    least two cameras and have passed either ASGARD’s fil-
    ters or visual inspection – are automatically analyzed
    on the server. The atmospheric trajectory is determined
    using the program MILIG (Borovicka, 1990); a full de-
    scription of the “straight least-squares method” can be
    found in that paper. The geocentric meteor position as
    a function of time in rectangular and WGS84 coordi-
    nates, the apparent meteor radiant in geocentric rect-
    angular and equatorial coordinates, the convergence an-
    gles, the topocentric azimuth and zenith distance, and
    the average atmospheric meteor speed are calculated
    and output by MILIG.
    The heliocentric orbit is calculated using the pro-
    gram MORB (part of the program FIRBAL; Ceplecha,
    1987). The average observed velocity is corrected for
    Earth’s rotation and gravity. The meteor radiant is
    also corrected and transformed to J2000 geocentric ra-
    diant coordinates. The heliocentric velocity and ecliptic
    latitude and longitude are calculated using the geocen-
    tric velocity and radiant position. The J2000 orbital
    elements follow from these quantities.
    The data pipeline and analysis are automated and
    meteor results are stored in a database; the most re-
    cent three weeks of data are available through a public
    websitea.

    The paper is WGN, the Journal of the IMO 48:3 (2020) pages 60 to 68.
    It's a black box. The description above does not give us any clue how the algorithms evaluate the uncertainty.

    In my experience, programmers often don't know how to do this correctly, so I wouldn't rely on it.

    As I said, "proper scientists", reporting measured results, would have a comprehensive uncertainty budget. Usually this would be evaluated according to the GUM, or if not, a good explanation should be given.

    The report should include a statement which gives the confidence range of the stated uncertainties.

    If it's any help, the total uncertainty depends overwhelmingly on the largest single uncertainties on the list. Often there is one variable in the calculation that has a much larger per cent uncertainty than all the others, and as a result, sometimes you can discount the smaller uncertainties as negligible.

  13. #13
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    Seven years of bright meteor data from the NASA All Sky Fireball
    Network
    Aaron Kingery 1, Danielle E. Moser 2, William J. Cooke 3, and Althea V. Moorhead 3,4
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    Looking deeper into the paper, I found where they say about interstellar meteors:

    The programs MILIG and MORB generate uncertainty
    estimates in the meteor’s trajectory. However, these
    values describe only the uncertainty in the orbital fit,
    and do not include sources of uncertainty such as errors
    in determining the center of light or distortion in the
    images near the horizon. Thus, they are strict under-
    estimates of the true uncertainty. They can be used as
    rough indicators of precision but should not be used to
    constrain, for example, the possible orbits for a partic-
    ular meteoroid. To illustrate this, we have computed
    the possible orbits corresponding to a meteor with 1-σ
    uncertainties of 5◦ in the ecliptic geocentric radiant and
    20% in the geocentric speed (see Figure 12). We find
    that these types of errors can result in a huge range
    of possible orbits and Tisserand parameters, and thus
    caution against using these data to study the dynam-
    ics of an individual meteoroid. We specifically warn
    against using these data to identify supposed interstel-
    lar meteoroids due to the lack of reliable uncertainties.
    However, these data can be used to study shower and
    sporadic meteor activity at large sizes, and occasionally
    to support meteorite hunts.

    Sorry for overlooking that before...
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    Quote Originally Posted by Tom Mazanec View Post
    Looking deeper into the paper, I found where they say about interstellar meteors:

    The programs MILIG and MORB generate uncertainty
    estimates in the meteor’s trajectory. However, these
    values describe only the uncertainty in the orbital fit,
    and do not include sources of uncertainty such as errors
    in determining the center of light or distortion in the
    images near the horizon. Thus, they are strict under-
    estimates of the true uncertainty. They can be used as
    rough indicators of precision but should not be used to
    constrain, for example, the possible orbits for a partic-
    ular meteoroid. To illustrate this, we have computed
    the possible orbits corresponding to a meteor with 1-σ
    uncertainties of 5◦ in the ecliptic geocentric radiant and
    20% in the geocentric speed (see Figure 12). We find
    that these types of errors can result in a huge range
    of possible orbits and Tisserand parameters, and thus
    caution against using these data to study the dynam-
    ics of an individual meteoroid. We specifically warn
    against using these data to identify supposed interstel-
    lar meteoroids due to the lack of reliable uncertainties.
    However, these data can be used to study shower and
    sporadic meteor activity at large sizes, and occasionally
    to support meteorite hunts.

    Sorry for overlooking that before...
    I notice it mentions "1-sigma uncertainties", which could mean the reported uncertainties are 1-sigma, corresponding to a 68% confidence uncertainty range. But it's possible I am making 2+2 =5 with this.

    Another worthwhile question is, does the calculation algorithm actually force a fit to a bound orbit?

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    I would say the program doesn’t...that’s how I thought there were unbound orbits in the first place. The “manual reduction” I don’t know.
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    Quote Originally Posted by Swift View Post
    Very frequently the +/- value is one, two, or three standard deviations, which for a normal distribution would include 68%, 95%, or 99.7% of the data, but as Grant says, you'd have to look at the reference to know if that is what they are reporting, and if it is a normal distribution.

    And yes, even if those values are three standard deviations, and it is a normal distribution, there is a chance that the value could be outside those limits.
    I agree completely with the above answer, although I will add a little bit to it. The "chance that the value could be outside those limits", from the second paragraph, is actually given in the first paragraph - if the range covers one standard deviation, it is about 0.32, if it covers two standard deviations, it is about 0.05, and if it covers three standard deviations, it is about 0.003.

    Note that if the estimate does have a normal distribution, the probability of being a large number of standard deviations off is extremely small - for example, it is about 2 in a billion for six standard deviations. A normal distribution has tails that go to zero very quickly - the probability of being far away from the estimated value is very very small.

    There is a result known as Chebyshev's inequality that can be used if the estimate has a non-normal distribution - it essentially gives you the "worst case" probability that the true value is outside the estimated range. The probability of being six or ten or some other large number of standard deviations away from the estimated value will be much higher using Chebyshev's inequality than assuming a normal distribution.

    Quote Originally Posted by grant hutchison View Post
    Eccentricity is not alway normally distributed (it depends on what orbits you're sampling), and I have to say that the numbers Tom has been posting scream "not normally distributed" to me, but that may be because Tom is sampling the tail of a sample.

    Grant HUtchison
    It is very likely that the underlying phenomenon does not have a normal distribution, but it is the distribution of the estimate, not the underlying phenomenon, that matters.

    To take an illustrative example, suppose I have a six-sided die, with the numbers 1 through 6 on each side. I want to estimate the average value produced by rolling the die. (Let's say, I'm not sure whether it is a "fair" die, or if it is weighted so that some numbers are more likely than others.) So suppose it is a fair die, but I don't know this, and want to determine it experimentally. So I throw the die a large number of times, and record the values.

    Now, since it is a fair die (even though I don't know this), the distribution of the data will be approximately uniform, which is very different than a normal distribution. It is discrete and bounded, with equal probability for all outcomes; the normal distribution is continuous, unbounded, and different ranges of values (of equal size) have different probabilities of occurring. So the outcomes produced by throwing the die do not conform well to a normal distribution at all.

    But, if I estimate the average value by adding up all of the die throws and dividing by the number of throws (a sample average), the distribution of this estimate is approximately normal, even for a relatively small number of die throws. For a large number of die throws, the distribution of the estimate is extremely close to normal.

    This is a consequence of the central limit theorem, which (warning: oversimplification) states that sample averages have approximately a normal distribution, regardless of the distribution of the underlying phenomenon. Given that, it is quite common to assume that a sample average has a normal distribution, whatever the distribution of the underlying phenomenon is. However, there are some assumptions needed for the central limit theorem to apply, so it sometimes doesn't work. Also, if the estimation method was something different than taking a sample average, then the central limit theorem would not apply.

    So the appropriateness of assuming normality does not depend only on the distribution of the underlying phenomenon (in this case, "eccentricity"), but also on the estimation method used. It's entirely possible that one person would use one estimation method where normality is a reasonable assumption for the distribution of the estimate, and someone else uses a different estimation method where it is not reasonable to assume normality.

    The other thing to keep in mind here is, the standard deviation is itself not known - it has to be estimated. Usually estimates of the standard deviation are called "standard errors", so it might be slightly more precise to use this terminology in Swift's answer (and also in my comments on it, although I'm not going to go back and correct my terminology). So there is not only uncertainty in producing the estimate itself, but also in estimating the standard deviation. We really can only get exact statistical results for very simple underlying distributions and simple estimation methods; in most cases, the best we can do is get so-called "asymptotic" results. That means the confidence interval is actually off somewhat, but as the dataset becomes larger, the error in the confidence interval becomes smaller. For a large enough data set, the error in determining the confidence interval can safely be ignored, but determining what is "large enough" can be more of an art than a science sometimes.

    So summing up, I think a highly relevant point is this one:

    Quote Originally Posted by grant hutchison View Post
    It'll be a confidence interval of some sort (which is to say, there will be a quantified probability that the true value lies outside the quoted +/- range). You need to look at the documentation to find out what it means, because different authors mean different things.
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    It sounds like hard work, sorting out candidate interstellar meteorites from this data and then trying to find them. It does not seem like you could say, this meteorite here, undeniably came from another stellar system based on the tracking data. But then again you could increase your chances of finding one.

    I've been thinking anyway, many thousands of meteorites have been found. We are also told in recent papers that interstellar objects passing through the solar system should not be uncommon. So is it not likely that some of the meteorites already in possession are interstellar? Has it always been simply assumed that all meteorites must have originated in the solar system?

  19. #19
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    Quote Originally Posted by 21st Century Schizoid Man View Post
    It is very likely that the underlying phenomenon does not have a normal distribution, but it is the distribution of the estimate, not the underlying phenomenon, that matters.
    Yes, I completely garbled that.
    I was thinking particularly of values like "5.587 +/- 4.855", quoted by Tom. Given that eccentricity doesn't have negative values, that seems like a set of symmetrical error bars being applied to an underlying distribution that isn't symmetrical.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Yes, I completely garbled that.
    I was thinking particularly of values like "5.587 +/- 4.855", quoted by Tom. Given that eccentricity doesn't have negative values, that seems like a set of symmetrical error bars being applied to an underlying distribution that isn't symmetrical.

    Grant Hutchison
    Yes, if we know from the physical nature of the quantity that it can't be negative, having zero be 1.15 standard deviations away from the estimate (assuming the 4.855 is one standard deviation) indicates a pretty strong deviation from normality in the distribution of the estimate.
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    Well, if you don't like my example you can see the specific, real world ones on the fireball thread: https://forum.cosmoquest.org/showthr...ireball-orbits
    Some of those are wide uncertainties, some narrow, but the email and paper say they were NOT hyperbolic.
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    Quote Originally Posted by Tom Mazanec View Post
    Well, if you don't like my example you can see the specific, real world ones on the fireball thread: https://forum.cosmoquest.org/showthr...ireball-orbits
    Some of those are wide uncertainties, some narrow, but the email and paper say they were NOT hyperbolic.
    How can they be so sure ?

    To know this with confidence, means that there are no calculated orbits with uncertainty bounds that include hyperbolic solutions.

    Do we actually know this to be the case?

    Also we need to take into account the stated uncertainties are minimum uncertainties; they have not done a full uncertainty budget. The correct uncertainty bounds would be larger than the stated uncertainties.

    Recent papers tell us there should be a certain density of interstellar bodies in the solar system. For any expected density of objects, there is a corresponding expectation number for the number that should land on Earth. Now, offhand, I have no clue of the magnitude of these numbers.

    There are 59,000 meteorites known to be in collections around the world.

    If the expectation is (for example) that 0.1% of meteorites are interstellar objects, that means our central expectation value is 59 interstellar objects already in collections. There is a Poisson uncertainty on this, which is approximately +/-15 at 95% uncertainty. So any number between 44 and 74 is reasonably consistent with the 0.1% expectation value.

    (Footnote: the 0.1% value is plucked out the air. to illustrate my idea I have no idea what this number should be).

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    I think they mean there are no confirmed hyperbolic (come to think of it, I am pretty sure this is what they meant...sorry).
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    Quote Originally Posted by Tom Mazanec View Post
    Well, if you don't like my example you can see the specific, real world ones on the fireball thread: https://forum.cosmoquest.org/showthr...ireball-orbits
    Yes, that's where I got the example I used above. I looked at the thread a couple of times before I realized you were just posting numbers, and my main conclusion after scanning the numbers was, "These data are a bit odd. I wonder what the error bars are supposed to represent."

    Grant Hutchison

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    Quote Originally Posted by Tom Mazanec View Post
    I think they mean there are no confirmed hyperbolic (come to think of it, I am pretty sure this is what they meant...sorry).
    That's a different thing to excluding all hyperbolic solutions. This is Type 1 and Type 2 errors:

    https://en.wikipedia.org/wiki/Type_I...s#Type_I_error

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    Hang on a minute I have just recalled something ! And that is, eccentricities >1 are hyperbolic.

    On the fireballs thread there is a list of objects with calculated orbits of E>1.

    While the uncertainties are high, I don't think it is unreasonable to suspect at least a fraction of these genuinely are hyperbolic.

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    Quote Originally Posted by kzb View Post
    Hang on a minute I have just recalled something ! And that is, eccentricities >1 are hyperbolic.

    On the fireballs thread there is a list of objects with calculated orbits of E>1.

    While the uncertainties are high, I don't think it is unreasonable to suspect at least a fraction of these genuinely are hyperbolic.
    Yes, Tom was posting those numbers because he thought they were hyperbolic.
    But he has since been authoritatively told otherwise.
    The problem appears to be that the quoted uncertainties are only one component of the overall uncertainties.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Yes, Tom was posting those numbers because he thought they were hyperbolic.
    But he has since been authoritatively told otherwise.
    The problem appears to be that the quoted uncertainties are only one component of the overall uncertainties.

    Grant Hutchison
    I'm not sure he has been told that. It seems to me some of the uncertainty bounds still include hyperbolic solutions even with this "manual reduction"?

    Also, from what we are told, there should be some interstellar objects.

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    IMVHO, that should have been made clear on the website. Herte is what the site says:

    Data: The cameras have overlapping fields of view, which means that the same fireball can be detected by more than one camera. This allows us to calculate the height of the fireball and how fast it is going. We can even work out the orbit of the meteoroid responsible for creating the fireball, which gives us clues about whether it came from a comet or an asteroid. If the fireball is traveling slow enough, and makes it low enough, it is possible that it can survive to the ground as a meteorite.

    Don't leave such an important consideration to one of thousands of articles in one of hundreds of journals.
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    The use of unqualified "+/-" by astronomers and physicists has long been a source of puzzlement and frustration to me.
    One of the fundamental rules of publishing medical research is that you keep the labels next to the numbers. So you'd write something like "Heart rate (Mean[SD]): 83[15]/min". It's so completely engrained it's almost a reflex.
    But I've lost count of the number of times I've had to rootle around trying to find out what the error bars mean when I'm look at astronomy publications.

    Grant Hutchison

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