Assignment Task :

Q1) 

Weather conditions influence the production of good quality coffee in a region. A list  of factors that influence the coffee cultivation, along with their possible values, and a  Bayesian network that represents the relationship between these factors (variables) are  given below.  

M (Maximum Temperature) ∈ { < 20, 20-30, 30-40, > 40 }  

N (Minimum Temperature) ∈ { < 0, 0-10, 10-20, > 20}  

W (Wind speed) ∈ {Low, Medium, High}  

H (Relative humidity) ∈ {< 50, 50-60, > 60}  

R (Precipitation) ∈ {Low, High} 

Solar

 

1.1) Write down the joint distribution #$%, ', (, ), *, +, for the above  network.  

1.2) Find the minimum number of parameters required to fully specify the  distribution according to the above network.  

1.3)  a) Write down a joint probability density function if there are no  independence among the variables is assumed.  

b) How many parameters are required, at a minimum, if there are no  independencies among the variables is assumed?  

c) Compare with the result of the above question (Q1.2) and comment.  

1.4) d-separation method can be used to find two sets of independent or  conditionally independent variables in a Bayesian network. For each of the  statements given below from (a) to (c), perform the following:  

• List all the possible paths from the first (set of) node/s to the second (set  of) node/s.  

 

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  • Posted on : October 23rd, 2018

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