Combining detection with other tasks of information processing

Classical detection theory, based on the Neyman–Pearson theorem provides the optimal rule for
deciding between two hypotheses concerning the distribution or density of a given observation or
sequence of observations. It tells us that best trade-off between the two kinds of probability of error
is achieved by the likelihood ratio test (LRT). In certain situations, however, this decision between
the two hypotheses might be only one of the tasks to be carried out. For example, consider a
scenario where under hypothesis H0, the sequence of observations that we receive is just pure noise
(or useless/irrelevant for any other reason), which contains no useful information that may interest
us, whereas under hypothesis H1, the data that we have at hand has emerged from a desirable
information source, and in this case, further processing is called for, such as lossless or lossy data
compression, parameter estimation channel decoding encryption, further classification, etc