For pattern recognition tasks, many times the data that is required to be analyzed and classified is a discrete vector of (sometimes assumed independent) components: **X** = (*x _{1}*,

As was seen in the continuous case of Bayes rule, the discrete case is much similar. However, instead of the feature vector x being a point in d-dimensional space, it now assumes one of *m* discrete values: *v _{1}*,...,

Furthermore, instead of utilizing *probability density functions *as was used if the random variable was continuous, the distribution is now a probability distribution or just a *probability*. Hence:

Nonetheless, as will be seen, the Bayes decision rule remains unchanged as it’s purpose is: to minimize the risk or cost in the decision.