So far, we have been given a probability event that belonged to one of a finite number of classes, for example, a temperature was classified as cold, warm, or hot. But how would we calculate the posterior probability if we were given the temperature in °C instead?
For this example, we are given the heights of five men and five women, as shown in the following table:
Height in cm | Gender |
180 | Male |
174 | Male |
184 | Male |
168 | Male |
178 | Male |
170 | Female |
164 | Female |
155 | Female |
162 | Female |
166 | Female |
172 | ? |
Suppose that the next person has a height of 172 cm. What gender is that person more likely to be, and with what probability?
One approach to solving this problem could be to assign classes to the numerical values; for example, the people with a height of between 170 cm and 179 cm would be in the same class. With this approach, we may end up with a few classes that are very wide, for example, with a high cm range, or with classes that are more precise but have...