## Contour as a verb

Our love is like the border between Greece and Albania – The Mountain Goats

(In which I am uncharacteristically brief)

Andrew’s answer to recent post reminded me of one of my favourite questions: how do you visualise uncertainty in spatial maps.  An interesting subspecies of this question relates to exactly how you can plot a contour map for a spatial estimate.  The obvious idea is to take a point estimate (like your mean or median spatial field) and draw a contour map on that.

But this is problematic because it does not take into account the uncertainty in your estimate.  A contour on a map indicates a line that separates two levels of a field, but if you do not know the value of the field exactly, you cannot separate it precisely.  Bolin and Lindgren have constructed a neat method for dealing with this problem by having an intermediate area where you don’t know which side of the chosen level you are on.  This replaces thin contour lines with thick contour bands that better reflect our uncertainty.

Interestingly, using these contour bands requires us to reflect on just how certain our estimates are when selecting the number of contours we wish to plot (or else there would be nothing left in the space other than bands).

There is a broader principle reflected in Bolin and Lindgren’s work: when you are visualising multiple aspects of an uncertain quantity, you need to allow for an indeterminate region.  This is the same idea that is reflected in Andrew’s “thirds” rule.

David and Finn also wrote a very nice R package that implements their method for computing contours (as well as for computing joint “excursion regions”, i.e. areas in space where the random field simultaneously exceeds a fixed level with a given probability).

1. Xi'an says:

I dream of a dynamic representation where these contours would fluctuate according to the degree of uncertainty…

2. Andrew says:

Dan,

This is an interesting application of a good general principle. Can we name the principle, so that it goes into the Lexicon?

• Dan Simpson says:

I quite like the “law of thirds” or the “law of three”.

If we were all Australian we could call it “Costello’s rule” after former Treasurer Peter Costello who famously urged Australian families to have more children: “One for mum, one for dad, one for the country”.