Markov Models EqUfuT3CC8s

Web Reference: In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state ... A Hidden Markov Model (HMM) handles exactly this situation. It has two layers: a hidden layer of states that follows the Markov property, and a visible layer of observations that each state produces. Speech recognition is a classic example. The words someone intends to say are the hidden states. The space on which a Markov process \lives" can be either discrete or continuous, and time can be either discrete or continuous. In Stat 110, we will focus on Markov chains X0; X1; X2; : : : in discrete space and time (continuous time would be a process Xt de ned for all real t 0). Most of the ideas can be extended to the other cases.

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