Examples of "multinomials"
Some of his work on multinomials was included by Maria Gaetana Agnesi, at Riccati's request, in the book on integral calculus of her "Analytical Institutions".
The concept translates to higher dimensions "D" if multinomials formula_62 in Cartesian coordinates are converted to hyperspherical coordinates, formula_63, multiplied by a product of Jacobi polynomials of the angular variables. In formula_64 dimensions, the angular variables are spherical harmonics, for example. Linear combinations of the powers formula_65 define an orthogonal basis formula_66 satisfying
With a multinomial event model, samples (feature vectors) represent the frequencies with which certain events have been generated by a multinomial formula_36 where formula_37 is the probability that event occurs (or such multinomials in the multiclass case). A feature vector formula_1 is then a histogram, with formula_39 counting the number of times event was observed in a particular instance. This is the event model typically used for document classification, with events representing the occurrence of a word in a single document (see bag of words assumption). The likelihood of observing a histogram is given by