To implement a backward memoryless Markov chain in MATLAB, you can use the backward algorithm. The backward algorithm is designed to calculate the probability of observing a set of future events given the current state of a Markov chain. Here's an example implementation:
main.m691 chars27 lines
In this implementation, P
is the transition matrix, B
is the emission probability matrix, pi0
is the initial state distribution, and O
is the sequence of observations. The beta
variable stores the backward probabilities for each state at each time step. The loop calculates the backward probabilities for each observation in reverse order, starting with the last observation. Finally, we calculate the probability of the entire sequence using the pi0
, B
, and beta
variables.
Note that this implementation assumes a discrete-time Markov chain with discrete emissions. There are more complex versions of the backward algorithm for continuous-time Markov chains and other types of emissions.
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