Principled Comparative Method - a new tool

[Jon Patrick]

Bob Whiting wrote on MOn 23 Aug

    You seem to be confused about what the topic of discussion is.
    Basically it is about measuring pathways of change between two
    daughter languages and a parent to see which of the daughters
    is closer to the parent *when all three are known*.  The method
    was described in a message posted by Jon Patrick on Thu, 12 Aug
    1999 (see http://listserv.linguistlist.org/cgi-bin/
    wa?A2=ind9908&L=indo-european&O=T&P=11528 for the message; note put this
    URL back together before using it).  Essentially the method is like
    counting up the little numbers between the stars on your Texaco road
    map to figure which route between two places is the shortest.  My
    comments were to the effect that the method could only be effective
    if all three languages were known and reconstruction of the parent was
    minimal (and not limited to the comparative method).

I'd just like to enhance Bob's descritpion of our method. There are some other
factors that contribute the quantitative statistic we arrive at. They are
1. The number of nodes in the network
2. The relative distributions of the outgoing arcs from each node.
There is a trade off between these two components such that the idea of a
minimum message length is meaningful. As you increase the number of nodes the
message length increases. However if the distributions on the outgoing arcs
become more regular then the message cost will go down. In fact we do the
computation in the opposite direction. We construct the canonical PFSA using
the whole data set then attempt to merge states. If the states under
comparison have similar distribution properties then the merge will produce a
smaller message cost, otherwise we don't do the merge.

Jon
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