# What is sensor matrices?

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What is sensor matrices?
One question.
I don’t understand the meaning of sensor matrices.Can somebody provide any hint?

We’re now talking about Hidden Markov Models, where the “current state” is not directly observable. Instead, you can only perceive certain evidence e_t at each time step t, where e_t gives you some information about the actual state of the world. Consequently, we need two probability distributions:

1. T, which gives you the probability that we’ll be in state Y at time (t+1) for each possible state X at time t, and
2. O, which gives you the probability that you will observe some piece of evidence e for each possible state X at time t.

O is the sensor matrix.

Recall the example with the umbrellas: You don’t know whether it rains or not, you only know whether some person (I think it was “the director”?) brought an umbrella or not. In order to estimate the probability that it’s raining today based on a series of observations of umbrellas (or no umbrellas), you need to know

1. The probability that if it rains at time t, it will also rain at time t+1 (this is encded as the matrix T) and
2. The probability that the director will carry an umbrella if it rains, and the probability they will carry an umbrella if it doesn’t rain. This is the sensor matrix.
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