[vsnet-alert 11035] Re: re CSS090201:090210-113032 : problematic 2MASScolours

Michael Linnolt linnolt at hawaii.edu
Tue Feb 3 04:36:03 JST 2009


Mine is a valid description of Malmquist effect or error, just as Brian put it too. Its really a simple thing in principle, I don't see the point of your belabored essay on the various alternate descriptions. 

The real problem is statistically proper (or not) data analysis and/or acquisition. It depends a lot on how you are defining the cutoff. If you set a fixed value for detection, and a faint observation with a wide error bar just touches that limit, is that a valid detection? Do we always know exactly how the data acquisition software is handling these cases? Is a detection set at 1, 2, 3 sigma, or the mean hitting the cutoff? This factor alone has a major impact on the degree to which Malmquist errors enter the data. 

Now, I don't want to open up the long old visual vs. CCD argument, but this is clearly an advantage that visual observing has over electronic. The visual observer sees a Poisson-like detection curve of a faint object at their limits. Usually, if a visual observer detects the object about 50% of the time thats considered the limit, but even a low detection percentage, say 10% can be used to make a reasonable estimate of the magnitude, not just simply "less-than". Electronic measurements typically set some arbitrary cutoff flux limit below which there is no detection at all, but the visual observer has no such arbitrary cutoff, and by using the abilities of the human eye-brain system, can uniformly respond to the entire range of Poisson-like detections with a valid magnitude estimate, down to the point of essentially 0% detectability. Of course, this is a "cut-off" too, but it is not subject to the statistical sampling error problems as described before.

Thus the seasoned visual observer using proper technique is going to provide better data at the instrumental limit as compared to electronic measurement.

Mike Linnolt

----- Original Message -----
From: varposts at Safe-mail.net
Date: Monday, February 2, 2009 10:52 am
Subject: [vsnet-alert 11034] Re: re CSS090201:090210-113032 : problematic 2MASScolours
To: vsnet-alert at ooruri.kusastro.kyoto-u.ac.jp

> -------- Original Message --------
> From: Michael Linnolt <linnolt at hawaii.edu>
> To: varposts at Safe-mail.net
> Cc: vsnet-alert at ooruri.kusastro.kyoto-u.ac.jp
> Subject: Re: [vsnet-alert 11030] re CSS090201:090210-113032 : 
> problematic 2MASScolours
> Date: Mon, 02 Feb 2009 09:41:45 -0800
> 
> > Need some clarification on this. Malmquist effect is a 
> sampling error due to arbitrary lower-limit flux cutoff of the 
> instrument (selection effect, affecting a number of observations 
> of objects). Not really biasing any given observation to appear 
> brighter...<
> No the Malmquist Effect is something else altogether.
> 
> But often astronomical measurement biases due to limits are 
> named after it, but the original Malmquist Effect has nothing to 
> do with instrumental limit fluxes directly.  The Malmquist 
> Effect was to do with a flux limited _object_sample_, which 
> gives a selection effect biasing towards only the brighter 
> objects being preferentially seen near the limit, but often folk 
> will use it re instrumental flux detection too.
> 
> The thing you describe, the lower limit flux cutoff, is what 
> causes a tendency on the whole for data in a dataset to be 
> brighter on average than they should be.  You usually 
> readily see this when you match two datasets of differing 
> limiting magnitudes, here's an old one
> 
> ftp://ftp.lowell.edu/pub/bas/VJT2mVJL.gif
> 
> Tycho2 V as per Tycho2 from VT and BT conversion tested against 
> LONEOS.PHOT literature sourced Vs for t'same stars, which goes 
> far deeper, you can see the trend there as Tycho2 limit is approached.
> 
> Basically, and very lamely, consider a measure not to be a point 
> with errors, but a roundish fuzzy statistical region in a 2D 
> 'magnitude space'.  If you make the threshold limit, the 
> flux limit, a rigid line (in actuality it too will be an 
> extended region, not just a 1D line, but it's complicated enough 
> already) then think in terms of photons you have it.
> 
> In each fuzzy round magnitude measure the photons going towards 
> making up the spread, each of different energy, are evenly 
> distributed around said fuzz.  Make the top half the more 
> energetic, higher intensity, photons, the bottom half the lower 
> intensity ones.  Now think of a round fuzz bissected by the 
> flux detection limit.  The ones below the threshold just 
> are not seen.  But the ones above are.  The photons 
> that are on average bright get kept, the ones on average faint 
> are totally lost, this biases the object towards looking 
> brighter than it is.
> 
> Not a fantastic analogy, but it's best I can do.
> 
> 
> Note again that Malmquist illustrated the bias about eighty 
> years ago to show a bias for brighter galaxies to be detected 
> over faint ones.  Granted this is somewhat due to the 
> limits of the telescopes used in any observing generation, ie is 
> connected to flux limited survyes, but is not strictly about 
> limitations of measures from a specific instrumental setup.
> 
> I can't find the Malmquist reference now.  I found it once, 
> and memory's telling me it was first noted by him in an 
> Astronomy Encyclopedia in 1928... ...however that memory could 
> well be wrong and I could be thinking about some other thing.
> 
> A quick google shows a nice review of Malmquist Bias in general 
> and it causing a selection effect here :-
> 
> http://astroprofspage.com/archives/81
> 
> Note I said "Malmquist Effect"-esque in my mail.  I've 
> asked around at times, pros and ams, as to what the actual 
> _mathematical_ term is for generic limit generated selection 
> effects, but everyone's just said that they tend to call it the 
> Malmquist Effect/Bias.
> 
> Summary : for an object at the faint limit remember that you 
> don't measure it's magnitude, you measure a probability space of 
> summed photons of varying intensity, and the stuff below the 
> faint limit doesn't get picked up, that above the limit does, 
> making the object appear brighter than is.  In practice 
> it's a sliding scale, a simple graph above illustrates the 
> increase in spread at faint mags, and the "handedness" towards 
> falsely bright of the spread due to this effect.  Not only 
> error increases, accuracy gets affected too.
> 
> And since I've been writing this, there's been Brian Skiff's 
> post too, and his end sentence "and the bias works in the sense 
> of picking up only on the statistically-spurious high values." 
> summarises it quite nicely.
> 
> Cheers
> 
> John


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