PROBABILITIES ON NATURAL LANGUAGE

             Anders Holtsberg

   Matematisk Statistik, Lunds Universitet


The sentence ``We saw a girl with a telescope''
ought to be more likely than the sentence ``We
telescope a saw with girl''. Also, in the former 
sentence the word ''saw'' has a probability close to
one for being a verb while in the second sentence it 
is more likely to be a noun (leaving the semantic 
difficulties of the verb version aside). I will 
give an overview of older as well as more recent 
methods of introducing probability measures on word 
sequences and estimating parameters in the models.
Especially I will say that most algorithms on hidden
Markov chains can be applied to hidden Markov trees.
 
The models often have extremely many parameters 
and the model selection problem has generated many 
interesting approaches. I will ask the question if
some of these approaches could not be utilized in
other fields, like time series analysis.