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Thread: Uncertainty

  1. #31
    Join Date
    May 2004
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    2,183
    Just to give another example, complete with context, here is the latest "hyperbolic" one:

    time 20210513 11.0068 hours
    lat 32 56 05.280 = 32.9348 deg
    lon 250 44 16.260 = 250.7378 deg
    ht 95.759 b -9.76770 -2.73044 -11.53669 -15.92146
    alp 344.717 +/- 1.158 deg
    del 7.163 +/- 2.142 deg
    v_inf 77.900 +/- 6.198 km/s
    v_avg 77.900 +/- 6.198 km/s

    a -0.841 +/- 0.512 AU
    e 1.829 +/- 0.564
    incl 156.482 +/- 4.087 deg
    omega 121.373 +/- 9.005 deg
    asc_node 52.613 +/- 0.001 deg
    v_g 76.770 +/- 6.263 km/s
    v_h 53.018 +/- 6.058 km/s
    alp_geo 344.574 +/- 1.170 deg
    del_geo 6.895 +/- 2.161 deg
    q_per 0.697 +/- 0.056 AU
    q_aph -2.379 +/- 0.976 AU
    lambda 348.810 +/- 1.395 deg
    beta 12.426 +/- 2.041 deg
    true anom 58.621 +/- 2.041 deg

    T_j hyp

    https://fireballs.ndc.nasa.gov/evcor...024D/orbit.txt
    https://fireballs.ndc.nasa.gov/evcor...024D/event.png
    Notice the "T_j hyp" whatever THAT means.

    Here is the complete email:
    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.

    That seems to say NO interstellar fireballs.
    This is saying definitely yes and definitely no. I give up.
    You are right, grant.
    SHARKS (crossed out) MONGEESE (sic) WITH FRICKIN' LASER BEAMS ATTACHED TO THEIR HEADS

  2. #32
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    Jul 2005
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    20,781
    It also quotes a negative semimajor axis, "a"--another quantity which can't actually go below zero. So these numbers, for whatever reason, are not saying anything we can directly translate to a real orbit.
    What your email is saying appears to be that none of the apparent hyperbolic solutions are hyperbolic within the limits of uncertainty, once all uncertainty has been considered--so there are no confidently hyperbolic orbits in the dataset. That doesn't mean there are no hyperbolics in the dataset, only that we can't identify any with [some level of] confidence, and that we cannot say [with some level of confidence] that any given fireball arrived along a barycentric hyperbolic orbit.

    So, basically, no point in getting excited about any particular number.

    ETA: The non-physical negative semimajor axis presumably reflects the geometrical relationship between a hyperbola and an ellipse.

    Grant Hutchison
    Last edited by grant hutchison; 2021-May-13 at 08:02 PM.

  3. #33
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    Apr 2005
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    Quote Originally Posted by grant hutchison View Post
    It also quotes a negative semimajor axis, "a"--another quantity which can't actually go below zero. So these numbers, for whatever reason, are not saying anything we can directly translate to a real orbit.
    What your email is saying appears to be that none of the apparent hyperbolic solutions are hyperbolic within the limits of uncertainty, once all uncertainty has been considered--so there are no confidently hyperbolic orbits in the dataset. That doesn't mean there are no hyperbolics in the dataset, only that we can't identify any with [some level of] confidence, and that we cannot say [with some level of confidence] that any given fireball arrived along a barycentric hyperbolic orbit.

    So, basically, no point in getting excited about any particular number.

    ETA: The non-physical negative semimajor axis presumably reflects the geometrical relationship between a hyperbola and an ellipse.

    Grant Hutchison
    That's what I've been trying to say, but probably not very well.

    However now we have the full email, it appears they are publishing erroneous data. If you can recalculate the same data manually, and get a completely different result to the computer, should you really be publishing the computer-generated result?

  4. #34
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    Jun 2009
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    Quote Originally Posted by Grey View Post
    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.
    Furthermore "that range" isn't a specific interval. "Confidence" is a property of a sampling process. It can't be interpreted as a probability applying to a single sample. For example, a sampling process may have 90% probability of producing an estimate that is within plus or minus 0.23 of a true population value. But if one application of the sampling process produces an outcome of 57, it is incorrect to to say that there is a 90% probability that the true value is in the interval (57 - 0.23, 57 + 0.23).

    In fact, the theory for computing a confidence interval for a parameter involves the assumption that the true value of the parameter has a fixed but unknown value. This contradicts the idea that the true value has a (non trivial) probability distribution. So, by the assumptions involved in computing confidence intervals, it is incorrect to assign the true value of the parameter a specific probability for being in a specific interval.

    Of course, almost everyone (mis)interprets confidence intervals and "error bars" etc. as if they indicate probabilities for the true values of parameters being in specific intervals. With the Bayesian model for a situation, one can find Bayesian "credible intervals" which allow the interpretation that people want to make. This involves assigning the true value of the parameter a specific "prior" probability distribution. That allows us to speak of the probability of the true value of parameter being in specific intervals.

  5. #35
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    423
    Quote Originally Posted by grant hutchison View Post
    It also quotes a negative semimajor axis, "a"--another quantity which can't actually go below zero.
    I thought that was the convention for hyperbolic trajectories.

    https://en.wikipedia.org/wiki/Hyperbolic_trajectory
    People who live in glass houses, should get undressed in the dark.

  6. #36
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    Jul 2005
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    Quote Originally Posted by 21st Century Schizoid Man View Post
    I thought that was the convention for hyperbolic trajectories.

    https://en.wikipedia.org/wiki/Hyperbolic_trajectory
    A negative semimajor axis makes sense mathematically, if we think of a hyperbola as a sort of inside-out ellipse, and you can plug it in to orbital energy calculations, but it doesn't have an inuitive physical meaning "on the ground". I was taught to use the pericentre distance (rp or q) as the scaling parameter for open orbits, which has the advantage of being a real-world measure that's easily visualized.
    I guess I shouldn't have used the word "translate" in my original comment, but I can't think of a better word. It is of course easy to mathematically "translate" the negative semi-major axis into a drawing of a hyperbolic orbit--the measure just doesn't readily translate into a mental image of a scaled hyperbola, at least not for me.

    But my formal training in this is more than four decades old, so I may be advocating an approach that is now deprecated. Wouldn't be the first time, probably won't be the last.

    Grant Hutchison

  7. #37
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    Dec 2018
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    Quote Originally Posted by tashirosgt View Post
    Furthermore "that range" isn't a specific interval. "Confidence" is a property of a sampling process. It can't be interpreted as a probability applying to a single sample. For example, a sampling process may have 90% probability of producing an estimate that is within plus or minus 0.23 of a true population value. But if one application of the sampling process produces an outcome of 57, it is incorrect to to say that there is a 90% probability that the true value is in the interval (57 - 0.23, 57 + 0.23).
    The only thing more galling than hearing people say critical things like this is - when they are right

    I am probably guilty of this myself in this thread (I didn't go back to check), but, yes, in classical terms, it is the confidence interval that is random, and the process for generating it should make sure it includes the true (but unknown) parameter value with probability 0.90 or 0.95 (or whatever the level of confidence is) for a randomly generated sample.
    People who live in glass houses, should get undressed in the dark.

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