So for an experiment I ended up needing conversions between 8 bits and 16 bits samples. To upscale an 8 bit sample to 16 bits, it is not enough to simply shift it by 8 bits (or multiply it by 256, same difference) because the largest value you get isn’t 65535 but merely 65280. Fortunately, stretching correctly from 8 bit to 16 bit isn’t too difficult, even quite straightforward.
In many occasions, we have to estimate a probability distribution from observations because we do not know the probability and we do not have enough a priori knowledge to infer it. An example is text analysis. We may want to know the probability distribution of letters conditional to the few preceding letters. Say, what is the probability of having ‘a’ after ‘prob’? To know the probability, we start by estimating frequencies using a large set of observations—say, the whole Project Gutenberg ASCII-coded English corpus. So we scan the corpus, count frequencies, and observe that, despite the size of the corpus, some letter combinations weren’t observed. Should the corresponding probability be zero?