Leonard Baum and his colleagues published a series of statistical papers introducing the hidden Markov model in 1960. These publications established the mathematical structure describing systems where observers see outcomes but cannot directly see the underlying process driving them.
The Viterbi algorithm efficiently calculates the maximum likelihood path through the state space to find the most likely sequence of hidden states given observed outputs. It evaluates joint probabilities for candidate sequences by multiplying transition and emission values.
Researchers rely on local optimization techniques like the Baum-Welch algorithm to derive maximum likelihood estimates from sets of output sequences when no exact algorithm exists. This method serves as a special case of the expectation-maximization algorithm that iteratively refines transition and emission probabilities until convergence occurs.
One of the first practical applications emerged in speech recognition starting around the mid-1970s. By the late 1980s, researchers began applying HMMs to analyze biological sequences, particularly DNA strands.
Hidden Markov models now support diverse fields ranging from computational finance to neuroscience including speech recognition systems and gene prediction tasks. They enable single-molecule kinetic analysis and assist cryptographers in breaking codes while helping scientists handle large datasets where traditional methods become too slow or inaccurate.