# Probabilistic Graphical Model

#### DV Man

##### New Member
I created a data frame from what the instructor gave me for my homework:

Code:
> cbind(Person.ID, Lerner.Alum, KJ, R)
Person.ID Lerner.Alum KJ R
[1,]         1           1  0 0
[2,]         2           0  0 0
[3,]         3           0  1 1
[4,]         4           1  1 0
[5,]         5           1  1 1
[6,]         6           0  0 0
[7,]         7           0  0 0
[8,]         8           0  1 0
[9,]         9           1  0 1
[10,]        10           0  1 1

"From the data shown above, calculate

P(LA = T, KJ = T, R = F)

where

LA: Lerner Alum

KJ: KnowsJunbo

R: Rich"

Can someone tell me what the commas signify in this example? I have tried searching the web but yet cannot find anything. My best guess is that it means that I should find all the times where all three occurrences (LA = T, KJ = T, R = F) happen, which would be 0.1, but this seems too simple for a 300 level course. Can anyone help? Thanks.

Also, I may have more questions after this, sorry

#### hlsmith

##### Omega Contributor
That would be my guess as well.

#### DV Man

##### New Member
Ok, thank you. I'll go with that for now until/unless someone reasons differently. For each question I have I will give my current thinking and approach to the problem.

For the next question, the instructor wrote:

"Using the same data, calculate

P(KJ = T)"

Again, I find it too simplistic, but I think I should just tally all the times where KJ was true, which is 0.5, and that would be the answer.

#### hlsmith

##### Omega Contributor
Perhaps these questions are basic for a reason, so that you can learn the fundamentals before delving into greater concepts.

Funny, in your first post I did not realize the T and F represented Boolean formatted variables. Makes more sense now. I recently learned about the associative rule in data mining. It seems equally basic to the above, but supposedly has decent properties.

#### DV Man

##### New Member
"Using the same data, calculate

P(R = T | KJ = T)"

I interpreted this as, find all the times R, or Rich is true, given that KJ, or Knowing Junbo is true. Thus, I had to look at all the times that KJ was true, and then see if R was true those times as well, giving me 0.3.

Does anyone see any wholes in my logic?

#### hlsmith

##### Omega Contributor
That is what I would do.

So no "wholes" in your logic, unless R = T for all times KJ = T; just kidding.

#### DV Man

##### New Member
That is what I would do.

So no "wholes" in your logic, unless R = T for all times KJ = T; just kidding.
Sorry, I am poor and come from a third-world country and am still getting acclimated to English. Also, I'm not poor, do not come from a third-world country, and just wanted to make you feel like an as\$hole.

Tough questions are coming. Be warned.

#### hlsmith

##### Omega Contributor
Yeah, I am probably the worst at spelling, of those who frequent this site. I just liked how the homophone still functioned to complete the sentence in a legible fashion.

#### DV Man

##### New Member
"We are interested in an event named 'Wet Grass.'

The Wet Grass event is denoted as W and it is affected by Sprinkler (S) and Rain (R).

Both Sprinkler and Rain can take True (T) or False (F) and they depend on the weather (Cloud (C)).

When C is T, obviously we have lower probability for S = T but higher probability for R = T.

The relationship among those random variables are illustrated in the probabilistic graphical model (PGM) below that I have attached.

Based on the PGM above, how many probabilities do we need to completely specify the full joint distribution?

What should be the value for a in the PGM?

What should be the value for b in the PGM?

From the PGM above, calculate:

P(W = T, S = T, R = T, C = T)

From the PGM above, calculate

P(S = T)"

Now, my thinking is that because there are 4 different columns with two options for each (T or F), the answer should be 2^4, or 16. What do you all think of that?

As for the value of a, I think it should be 0.1, and the value of b should be 0.3, since they both have to sum up to 1. That one was admittedly easy.

Lastly, the last two questions are kind of tricky. For the first one, I did 0.5 (C =T) * 0.1 (S = T) * 0.7 (R = T) * 0.99 (W = T) to give me 0.03465. Intuitively, this seems right, as it is not very likely at all that the sprinklers would be on when it's raining.

The last one is throwing me fits. Does anyone have any guesses?

#### DV Man

##### New Member
Also, those were the last questions. I thank you for the help, but am reminded that I am not done as I still need to figure out those last couple of questions...
[video]https://youtu.be/bW7Op86ox9g[/video]

#### hlsmith

##### Omega Contributor
I would love to take this class. Is it just called PGM? So it is an upper undergrad course?

I don't have time right now to stare at this problem, but it is a very popular problem with probably derivatives online. They also use a broken bottle getting the ground wet. This problem will also come up when you get to Berkson Bias, or how S and R are independent, but if you control for W then you have information on the other variable even though it is independent.

Do you have you all's syllabus that you can make available. I am curious what text you will use and the content for the class. Bunches will probably be taken from Pearl and Koller's books.

Haven't really thought about your problems, but due to Markov Process Decision, many times you don't have to control for C in the model since it is an antecedent with no other direct affect on W not through S and R.

#### DV Man

##### New Member
I would love to take this class. Is it just called PGM? So it is an upper undergrad course?

I don't have time right now to stare at this problem, but it is a very popular problem with probably derivatives online. They also use a broken bottle getting the ground wet. This problem will also come up when you get to Berkson Bias, or how S and R are independent, but if you control for W then you have information on the other variable even though it is independent.

Do you have you all's syllabus that you can make available. I am curious what text you will use and the content for the class. Bunches will probably be taken from Pearl and Koller's books.

Haven't really thought about your problems, but due to Markov Process Decision, many times you don't have to control for C in the model since it is an antecedent with no other direct affect on W not through S and R.
It's BUAD345: Data Analytics and Visualization, at the University of Delaware. There's no textbook. The syllabus is kind of lame but you can take a look.

Thanks for the input thus far. I'm going back to studying for Marketing for the time being, but I'll eventually look at the last question in detail again. I saw a variation of the problem on Wikipedia, but it didn't include the clouds variable. Let me know if you get anything else. Thanks

#### DV Man

##### New Member
I would love to take this class. Is it just called PGM? So it is an upper undergrad course?

I don't have time right now to stare at this problem, but it is a very popular problem with probably derivatives online. They also use a broken bottle getting the ground wet. This problem will also come up when you get to Berkson Bias, or how S and R are independent, but if you control for W then you have information on the other variable even though it is independent.

Do you have you all's syllabus that you can make available. I am curious what text you will use and the content for the class. Bunches will probably be taken from Pearl and Koller's books.

Haven't really thought about your problems, but due to Markov Process Decision, many times you don't have to control for C in the model since it is an antecedent with no other direct affect on W not through S and R.

#### DV Man

##### New Member
Has anyone gotten any further on the last question?

#### DV Man

##### New Member
I submitted the test and got a 9/10, the last one being the one I got wrong. I said 0.1, given that it would be 0.5 (C= T) * 0.1 (S = T, C = T) / 0.5 (C = F). Can someone tell me where I erred?

#### DV Man

##### New Member
I also know that it cannot be 0.2, as that was my first submission