### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 4aPP9. Probability theory and speech perception.

**Arthur Boothroyd
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*City Univ. of New York, 33 W. 42 St., New York, NY 10036
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Fletcher recognized the value of probability theory in developing a
quantitative approach to speech perception---hence the articulation index (AI).
He also recognized the need to allow for violations of the independence
assumptions that underly basic probability theory. For example, in nonsense
syllables, the probability (p[sub w]) of recognizing a word equals p[sub p][sup
n], where p[sub p] is the probability of recognizing the constituent phonemes
and n is the number of phonemes per word. In real words, however, p[sub
w]=p[sub p][sup j], where n(greater than or equal to)j(greater than or equal
to)1. Similarly, extending the methods of AI, the probability of recognition of
words in sentences ([sup s]p[sub w]) can be shown to be related to the
probability of recognition in isolation ([sup i]p[sub w]) by the equation [sup
s]p[sub w]=1-(1-[sup i]p[sub w])[sup k], where k is an exponent reflecting the
contribution of the sentence context. From these two basic equations one can
derive relationships among many measures of speech perception, ranging from the
phonetic level to the sentence level. The empirical values of the exponents j
and k can be used both to quantify the effects of various structural and
contextual constraints and to assess an individual's use of those constraints.
[Work supported by NIDCD Grant No. 10078.]