“HMMs are at the heart of speech-recognition systems like Siri. In speech recognition, the hidden states are written words, the observations are the sounds spoken to Siri, and the goal is to infer the words from the sounds. The model has two components: the probability of the next word given the current one, as in a Markov chain, and the probability of hearing various sounds given the word being pronounced. (How exactly to do the inference is a fascinating problem that we’ll turn to after the next section.) Siri aside, you use an HMM every time you talk on your cell phone. That’s because your words get sent over the air as a stream of bits, and the bits get corrupted in transit. The HMM then figures out the intended bits (hidden state) from the ones received (observations), which it should be able to do as long as not too many bits got mangled. HMMs are also a favorite tool of computational biologists. A protein is a sequence of amino acids, and DNA is a sequence of bases. If we want to predict, for example, how a protein will fold into a 3-D shape, we can treat the amino acids as the observations and the type of fold at each point as the hidden state. Similarly, we can use an HMM to identify the sites in DNA where gene transcription is initiated and many other properties.”