From the diagram, it is clear that the conditional probability distribution of the hidden variable x(t) at time , given the values of the hidden variable at all times, depends only on the value of the hidden variable ; the values at time and before have no influence. This is called the Markov property. Similarly, the value of the observed variable y(t) depends on only the value of the hidden variable x(t) (both at time ).
From the diagram, it is clear that the conditional probability distribution of the hidden variable x(t) at time , given the values of the hidden variable at all times, depends only on the value of the hidden variable ; the values at time and before have no influence. This is called the Markov property. Similarly, the value of the observed variable y(t) depends on only the value of the hidden variable x(t) (both at time ).