Pattern Recognition, 4th Edition

5.4.1. Hypothesis Testing Basics

Let x be a random variable with a probability density function, which is assumed to be known within an unknown parameter θ. As we have already seen in Chapter 2, in the case of a Gaussian, this parameter may be the mean value or its variance. Our interest here lies in the following hypothesis test:The decision on this test is reached in the following context. Let xⁱ, i = 1, 2,…, N, be the experimental samples of the random variable x. A function f(·,…,·) is selected, depending on the specific problem, and let q = f(x¹, x²,…, x^N). The function is selected so that the probability density function of q is easily ...