# Hidden Markov Model with likelihood sampling method

I have a revision question for an exam which I'm unsure about. The question includes Hidden Markov Model which I'm well aware of, but I'm just not sure how to use the weighted sampling method in this scenario. Would appreciate some help :)

The question states:

The HMM depicts a scenario. In this model, there are a sequence of latent(unobserved) random variables {R0,R1,··· ,RT} which represent if it is raining outside and a sequence of observed random variables (evidence) {U0,U1,··· ,UT} indicating whether the director arriving with an umbrella. Here, we use Rt = True denotes raining and Ut = True represents that an umbrella is observed. We deﬁne the following probabilities:

• P(R0 = True) = 0.2
• P(Rt = True|Rt−1 = True) = 0.7
• P(Rt = True|Rt−1 = False) = 0.3
• P(Ut = True|Rt = True) = 0.9
• P(Ut = True|Rt = False) = 0.2 We are interested in estimating the distribution of P(RT|U0,U1,··· ,UT). To calculate this distribution, you are required to use likelihood weighted sampling method to perform the approximate inference.

Any comments regarding the above problem will be appreciated. Thanks

• What is your question? What do you have so far? Are you sure this is proper place for your question? It looks like pure math or statistics. – Evil Jun 10 '18 at 6:01