By Alder M.
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Extra info for An Introduction to Pattern Recognition
Html (5 of 6) [12/12/2000 4:04:14 AM] Parametric data, and some will be discussed later. The (Bayesian) use of the likelihood ratio to select the best bet has its own rationale, which can extend to the case where we have some prior expectations about which category is most likely. Again, we shall return to this in more detail later. html (6 of 6) [12/12/2000 4:04:14 AM] Non-parametric Next: CART et al Up: Statistical Methods Previous: Parametric Non-parametric Suppose we assume that there is some probability density function (pdf for short) for the men and another for the women, but we are unwilling to give a commitment to gaussians or any other family of functions to represent them.
Indeed, we can say how much more likely by looking at the ratio of the two numbers, the so called likelihood ratio Moreover, we can fairly easily tell if a point is a long way from any data we have seen before because both the likelihoods and will be small. What `small' means is going to depend on the dimension, but not on the data. 10. shows a new point, and the two gaussian functions sitting over it; the argument that says it is more likely to belong to the function giving the greater height may be quantified and made more respectable, but is intuitively appealing.
Html (1 of 6) [12/12/2000 4:04:14 AM] Parametric The distribution of heights of a sample of men may be modelled approximately by the gaussian function in dimension 1 for suitably chosen values of . The modelling process means that if you want an estimate of the proportion of the sample between, say, 170 and 190 cm. tall, it can be found by integrating the function between those values. The gaussian takes only positive values, and the integral from to is 1, so we are simply measuring the area under the curve between two vertical lines, one at 170 and the other at 190.
An Introduction to Pattern Recognition by Alder M.