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David Weenink co-created Praat with Paul Boersma, providing tools for measuring and modeling speech. His 2006 thesis investigated speaker-adaptive vowel identification: how recognition can remain useful when acoustic patterns vary between speakers.^[ref][ref]

The thesis describes recordings from 30 speakers, each producing 12 Dutch vowels in controlled sentence frames. It relates these data to formants, principal component analysis, discriminant analysis and adaptive classification methods. This makes the recognition problem experimentally concrete: a classifier must separate vowel identity from speaker-related variation rather than memorize a single speaker's frequency spectrum.^[ref]

Homepage: www.fon.hum.uva.nl/david/

Discriminant analysis constructs statistical rules distinguishing labelled classes from their measured feature values. A common generative approach models the class-conditional probability distribution and applies Bayes' theorem to compare posterior class probabilities. Linear discriminant analysis uses multivariate normal distributions with a shared covariance matrix; allowing a different covariance matrix for each class gives quadratic discriminant analysis.^[ref]

For two equally likely one-dimensional classes, suppose $X\mid C_1\sim N(0,1)$ and $X\mid C_2\sim N(2,1)$. Their log-likelihood ratio isChoosing the larger posterior therefore selects $C_2$ for $x>1$, with a tie at one. Different class probabilities move this threshold. Estimating means and covariance from training data supplies a fitted rule, while independent evaluation tests whether its assumptions generalize.