Pattern Recognition, 4th Edition

2.4. Bayesian Classification for Normal Distributions

2.4.1. The Gaussian Probability Density Function

One of the most commonly encountered probability density functions in practice is the Gaussian or normal probability density function. The major reasons for its popularity are its computational tractability and the fact that it models adequately a large number of cases. One of the most celebrated theorems in statistics is the central limit theorem. The theorem states that if a random variable is the outcome of a summation of a number of independent random variables, its pdf approaches the Gaussian function as the number of summands tends to infinity (see Appendix A). In practice, it is most common to assume that the sum of random variables ...