Consider a temporal process where the state variables at time t depend directly not only on the…

Consider a temporal process where the state variables at time t depend directly not only on the variables at time t − 1, but rather on the variables at time t − 1, . . . , t − k for some fixed k. Such processes are called semi-Markov of order k.

a. Extend definition 6.3 and definition 6.4 to richer notions, that encode such a kth order semi-Markov processes.

b. Show how you can convert a kth order Markov process to a regular (first-order) Markov process representable by a DBN over an extended set of state variables. Describe both the variables and the transition model.

Definition 6.3

A 2-time-slice Bayesian network (2-TBN) for a process over X is a conditional Bayesian network over X’ given X_I, where X_I ⊆ X is a set of interface variables.

Definition 6.4

A dynamic Bayesian network (DBN) is a pair, where B₀ is a Bayesian network over X(0), representing the initial distribution over states, and B_→ is a 2-TBN for the process. For any desired time span T ≥ 0, the distribution over X (0:T) is defined as a unrolled Bayesian network, where, for any i = 1, . . . , n:

• the structure and CPDs of X⁽⁰⁾_i are the same as those for X_i in B₀,

• the structure and CPD of X^(t)_i for t > 0 are the same as those for X⁰_i in B_→.

 

 

Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount!
Use Discount Code “Newclient” for a 15% Discount!

NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you.

The post Consider a temporal process where the state variables at time t depend directly not only on the… appeared first on Affordable Nursing Writers.