betsyrocamora said:Can someone help me with this question.
Let us define a Markov hidden model with 2-states A and B, such that
P(X0=A)=0.6,P(X0=B)=0.4,P(X1=A/X0=A)=0.3,P(X1=B/X0=B)=0.8
what is the value of P(X3=A) ??
I like Serena said:Welcome to MHB, betsyrocamora! :)
This looks like a question that is intended to learn what a hidden Markov model actually is.
Do your notes perhaps contain a worked example?
Or perhaps an example for a Markov chain?
betsyrocamora said:No, I know what is a hidden markov model, but with this one I am a little lost, I have tried to let j denote the state A. Used p3ij:=P(X3=j|X0=i) that satisfies the Chapman Kolmogorov equations and after that I think is the total probabilities ecuation but I am lost in there hahha
A Hidden Markov Model is a statistical model used to predict the probability of a sequence of unobservable or hidden states based on a sequence of observable outcomes. It is used in a variety of fields, including speech recognition, pattern recognition, and bioinformatics.
A Hidden Markov Model works by using a set of observed data to estimate the probability of a sequence of hidden states. This is done through a process called the forward-backward algorithm, which calculates the probability of each hidden state at each time step based on the previous state and the observed data.
The main difference between a Hidden Markov Model and a regular Markov Model is that in a Hidden Markov Model, the states are not directly observable. Instead, they are inferred from the observed data. This makes HMMs more flexible and useful for modeling complex processes.
Hidden Markov Models have a wide range of applications, including speech recognition, handwriting recognition, protein structure prediction, and financial market analysis. They are also commonly used in natural language processing tasks such as part-of-speech tagging and language generation.
While Hidden Markov Models are useful in many scenarios, they do have some limitations. They assume that the underlying system is stationary and that the observations are independent of each other. They also require a large amount of training data and can struggle with long sequences of data. Additionally, HMMs are limited in their ability to capture complex relationships between hidden states and observations.