Principled Comparative Method - a new tool

[Jon Patrick]

    Date:       Wed, 25 Aug 1999 21:56:02 -0400 (EDT)
    From:       Sean Crist <kurisuto at unagi.cis.upenn.edu>

On Wed 25 Aug Sean Crist responded to

    On Tue, 24 Aug 1999, Robert Whiting wrote:

    > And it is incorrect to describe "In the best case it [a reconstruction]
    > is only the statistically most probable original relationship between
    > the forms found in the daughter languages" as a statement about the
    > comparative method.  Please read what is said before going into
    > knee-jerk reactions.  Nothing was said about the comparative method.

    All right.

    If I'm recalling correctly, the author of the original message said that
    one of the things he was measuring was the "distance" between attested
    forms and reconstructed forms.  Since the Comparative Method is the only
    widely accepted method for reconstructing prehistoric forms, I assumed
    that the writer was going with reconstructed forms produced by the
    Comparative Method.  You're right, tho, that he didn't specify that this
    is the case.

I can't remember my exact words but I would like to clarify that we have only
used the method on attested languages -MIddle Chinese to Beijing and Cantonese
. However I offer the conjecture that the method is also useful for assisting
in discrimination between COMPETING reconstructions. That is it would tell
which reconstruction would be statistically closest to its daughter given the
particular dataset available. It also has potential to give some illumination
to the systemic structure of the reconstructionS.

    I understand the idea of computing an optimal path perfectly well, and
    I've understood from the start of the thread that this was the methodology
    being employed.  My question is this: exactly what happens during the
    transitions in the probabilistic automata, and how are the probabilities
    for the transitions determined?

    Automata normally perform a concatenation operation across each arc
    between states.  One can imagine an automaton-like machine where the
    transitions can perform other sorts of operations, such as an umlaut rule
    (i.e., context sensitive substitutions). I'm not sure whether it's proper
    to use the term "automaton" to describe this richer sort of machine.  But
    if the machine in question is strictly concatentative (as automata at
    least canonically are), I'm puzzled as to how you would model historical
    sound change in such a machine, since historical sound change isn't
    concatenative.

I think you may be confounding the notions of an automata and a transducer. An
automata more restrcitively is considered as a descritpion of a set of states
and symbols that appear in an input stream that activate a transition to a
next state. These automata are used often to initiate other computation but
that usually is not considered to be part of the automata. A transducer is
considered to be something that applies a rule to that transition symbol.
Perhaps that's what you are thinking of.
The probablities in the PFS Automata come from counting the number of times
the transition is made to parse the full dataset. Note the dataset in our case
is NOT actually the mother+daughter words but rather the diachronic
phonological rules for each word pair. We don't do anything with the rules -
we just treat them as a transition symbol.

Jon Patrick
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