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cs-677sp2010:decisions-lab [2014/12/12 20:40] (current)
ryancha created
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 +== Discrete EVSI ==
  
 +'''​Do this one by hand''',​ but you can check it with your code if you really want to. This is like the oil example from class.
 +
 +=== Discrete Expected Utility ===
 +
 +let $P\left(x\right) = 0.2$ for a Boolean Random Variable X.
 +
 +Assume that you have your choice between two utilities, both functions of X:
 +
 +$U\left(1,​x\right)= 400$ and $U(1,\neg x)= 2$
 +
 +$U\left(2,​x\right)= 20$ and $U(2,\neg x)= 100$
 +
 +Compute the Expected Utilities and state what choice you would make.
 +
 +=== Conditional Expected Utilities ===
 +
 +Suppose that X influences another Random Variable, Y, in the following way:
 +
 +$p\left(Y=1|x\right) = 0.2$
 +
 +$p\left(Y=2|x\right) = 0.4$
 +
 +
 +$p(Y=1|\neg x) = 0.6$
 +
 +$p(Y=2|\neg x) = 0.3$
 +
 +Note that Y can take three values 1,2, or 3
 +
 +Compute the conditional probabilities:​
 +
 +Note that we will be computing many probabilities in this and subsequent sections. You may compute the joint of x and y and then sum the needed Values out of your joint or use Bayes' law directly.
 +
 +* $p\left(x|Y=1\right)$
 +* $p\left(x|Y=2\right)$
 +* $p\left(x|Y=3\right)$
 +
 +Use these probabilities to compute the conditional expected utilities:
 +
 +* $E\left(U\left(1,​x\right)|Y=1\right)$
 +* $E\left(U\left(2,​x\right)|Y=1\right)$
 +* $E\left(U\left(1,​x\right)|Y=2\right)$
 +* $E\left(U\left(2,​x\right)|Y=2\right)$
 +* $E\left(U\left(1,​x\right)|Y=3\right)$
 +* $E\left(U\left(2,​x\right)|Y=3\right)$
 +
 +What choice would you make in each of the following cases '''​and'''​ what utility would you expect in each case.
 +
 +* Y=1
 +* Y=2
 +* Y=3
 +
 +=== Expected Value of Sample Information ===
 +
 +Compute the following probabilities:​
 +
 +* $p\left(Y=1\right)$
 +* $p\left(Y=2\right)$
 +* $p\left(Y=3\right)$
 +
 +What is the Expected Posterior Utility?
 +What is the Expected Value of Sample Information?​
 +
 +This sequence of questions led you through the computations needed for EVSI. Please note that if I were to put an EVSI question on the test, I would '''​not'''​ lead you through the computation step by step as I have done here. You will need to understand the process on your own. You may also get a slightly more complex net (like with 3 nodes).
 +
 +== Burglar Alarm ==
 +
 +The Burglar Alarm example is described on pages 493 and 494 in Russell and Norvig. ​ If you don't have the book, look at slides 5 and 6 on [http://​www.d.umn.edu/​~rmaclin/​cs8751/​Notes/​chapter14a.pdf this pdf].
 +
 +Suppose that the city of Berkley charges $25 for the police to respond to a false alarm and that the deductible on the insurance for burglaries is $1000. Should I call the police if John calls me? If Mary calls? If both call?
 +
 +Now suppose that I can call the alarm company and find out if the alarm is going off for a fee (x dollars). For what values of x (if any) is it worth calling the alarm company if Mary has called? Note that you do not need to find the '''​exact'''​ cut off point, plot the net expected utility for maybe 10 possible x's that show the cut off point.
 +
 +'''​Please use your mcmc code to answer this question'''​. You may want to add a little code to automate the collection of expected utilities. Please think carefully about how to use your code to solve this problem. ​
 +
 +== Continuous Expected Utility ==
 +
 +This is just a continuous expected utility.
 +
 +If you find yourself actually trying to solve the integral using your calculus book, you have forgotten to apply a something you know about expectations!  ​
 +
 +'''​Do this by hand'''​
 +
 +Suppose:
 +
 +:$\theta \sim N\left(1,​2\right)$
 +
 +
 +:​$U\left(1,​\theta\right)=\frac{1}{4}\cdot \theta + 4$
 +
 +
 +:​$U\left(2,​\theta\right)=-2\cdot \theta + 4$
 +
 +What decision would you make?
 +
 +== Continuous EVSI ==
 +
 +'''​Do this by hand'''​ (see the [[Continuous EVSI]] page for help)
 +
 +Using the model from class for normally distributed $\theta \sim N\left(1,​2\right)$ (as above) and $y \sim N\left(\theta,​2\right)$ with linear cost functions as given above, compute the EVSI.
 +
 +You may use a stats package or a www applet (or a book!!) to compute $\phi\left(z\right)$ and $\Phi\left(z\right)$.
cs-677sp2010/decisions-lab.txt ยท Last modified: 2014/12/12 20:40 by ryancha
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