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    Re: Still on LOPs
    From: George Huxtable
    Date: 2002 Apr 18, 20:45 +0100

    Peter Fogg writes-
    
    >If we have just one LOP then I can see that the possibility is 50/50
    >that the real position (RP) lies on either side of it. But I suspect
    >that with a second and third, the probability of the  RP lying within
    >the confines of the LOPs increases, not decreases. This is what common
    >sense and long experience tells us and the elliptical plots we've seen
    >seem to bear this out.
    >
    >I suspect that George Huxtable is having a lend of us by trying to show
    >the contrary, a classic case of 'lies, damn lies and statistics',
    >although its all to the good by forcing us to think about the question
    >and justify it by all means possible.
    
    ===============
    
    To Peter Fogg, the conclusion (that the probability of the real position
    being inside the cocked hat is only 25%) may be intellectually abhorrent,
    but he will have to present better arguments if he wants to shoot it down.
    
    Presumably, having agreed that with one LOP the probability of the real
    position lying on one side or the other is split 50/50, he accepts that
    this is also true for any other LOP, as these measurements are quite
    independent of each other. The conclusion inevitably follows.
    
    When Peter says "with a second and a third, the probability of the RP lying
    within the confines of the LOPs increases, not decreases", I do not
    understand this. Until the third LOP has been drawn, to produce a triangle,
    there are no "confines" to contain the real position. So what exactly is he
    arguing?
    
    I am all for giving due weight to "common sense and long experience", but
    against the demands of simple logic, Peter has to apply argument and reason
    to defend his position.
    
    Peter says-
    >I suspect that George Huxtable is having a lend of us by trying to show
    >the contrary, a classic case of 'lies, damn lies and statistics'
    
    Well, I must admit to getting some enjoyment from confounding the
    conventional wisdom, but it is not entirely mischief-making. There are many
    navigators around who firmly believe that when they draw a cocked hat,
    their true position must lie inside it. If they can be convinced of the
    truth, that the true position is three times more likely to be outside the
    triangle than inside it, they will reinterpret their plots with greater
    understanding. And that can only do good.
    
    By the way, my introduction to this "cocked hat" problem came from an Open
    University programme on statistics, which was broadcast on TV in the UK,
    perhaps 20 years ago. I have not seen it discussed in a text on navigation,
    except in "From Sails to Satellites", by JED Williams, Oxford University
    Press, 1992.
    
    George Huxtable.
    
    ------------------------------
    
    george---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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