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I want to make current day depends on a random days rather than yesterday or depends on specified past days for example two days, then change bayes equations

but my talent is not enough to deal with these, i am glad if there is some examples for me to follow, or direct me to another advanced topics besides markov

if i am know that today depends on some days such as 3 days before, 5 days before how bayes would be?

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every process with a finite memory is a Markov process over an extended state space – Ilya Jan 18 '13 at 12:53
does you mean depends on yesterday or depends on 3 days before yesterday are the same? i do not know about extended state space, why only depends on yesterday, how about random a day? – Scott Jan 18 '13 at 13:03
up vote 2 down vote accepted

Processes such that the state at time $t+1$ depends on the states between times $t-D_t$ and $t$, where $D_t$ is random, are called variable length Markov chains (VLMC).

The canonical reference on this is a paper by Bühlmann and Wyner, available here and published in The Annals of Statistics in 1999. A link with probabilistic dynamical source models is established in 2002 in this paper by Cénac et al.

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what is the name of paper 2002, can not see now – Scott Jan 19 '13 at 10:34
@Scott Changed the link, sorry about the inconvenience. – Did Jan 19 '13 at 11:41

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