Question

Likelihood of the First Model 1 point possible (graded) For simplicity, assume that our vocabulary $ W $ consists of just two symbols 0 and 1 , i.e. $ W=\{0,1\} $. We want to estimate a multinomial model to generate a document $ D= $ "0101". For this task, we consider two multinomial models $ M_{1} $ and $ M_{2} $ with parameters, $ \theta^{(1)} $ and $ \theta^{(2)} $ respectively. First consider a multinomial model $ M_{1} $ with parameters $ \theta^{(1)} $ given as follows: \[ \theta_{0}^{(1)}=\frac{1}{2}, \theta_{1}^{(1)}=\frac{1}{2} \] Let the probability of model $ M_{1} $ generating the document $ D $ be denoted by $ P\left(D \mid \theta^{(1)}\right) $. Enter the value of $ P\left(D \mid \theta^{(1)}\right) $ given that $ \theta^{(1)} $ takes the values as described above. Enter your answer below as a numerical expression or round it off to four decimal places. $ \square $

          Likelihood of the First Model
1 point possible (graded)
For simplicity, assume that our vocabulary \( W \) consists of just two symbols 0 and 1 , i.e. \( W=\{0,1\} \).
We want to estimate a multinomial model to generate a document \( D= \) "0101".
For this task, we consider two multinomial models \( M_{1} \) and \( M_{2} \) with parameters, \( \theta^{(1)} \) and \( \theta^{(2)} \) respectively.
First consider a multinomial model \( M_{1} \) with parameters \( \theta^{(1)} \) given as follows:
\[
\theta_{0}^{(1)}=\frac{1}{2}, \theta_{1}^{(1)}=\frac{1}{2}
\]

Let the probability of model \( M_{1} \) generating the document \( D \) be denoted by \( P\left(D \mid \theta^{(1)}\right) \).
Enter the value of \( P\left(D \mid \theta^{(1)}\right) \) given that \( \theta^{(1)} \) takes the values as described above. Enter your answer below as a numerical expression or round it off to four decimal places.
\( \square \)

$Likelihood of the First Model 1 point possible (graded) For simplicity, assume that our vocabulary W consists of just two symbols 0 and 1 , i.e. W={0,1}. We want to estimate a multinomial model to generate a document D= "0101". For this task, we consider two multinomial models M1 and M2 with parameters, θ^(1) and θ^(2) respectively. First consider a multinomial model M1 with parameters θ^(1) given as follows: θ0^(1)=(1)/(2), θ1^(1)=(1)/(2) Let the probability of model M1 generating the document D be denoted by P(D |θ^(1)). Enter the value of P(D |θ^(1)) given that θ^(1) takes the values as described above. Enter your answer below as a numerical expression or round it off to four decimal places. □$

Added by Stacy P.

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