PSet 20: Bayesian Networks
(videos: Inference and Example Inference (BBN-VE-example)
Imagine you live in San Diego in a nice bungalow, with two friendly neighbors John and Mary, who live on either side. You all live in an OK neighborhood, but you’ve installed an alarm system just in case. Now, sometimes there are burglaries, and those set off alarms with certain probabilities, but you also live in earthquake country, and sometimes there are earthquakes, which can also set off alarms. If your alarm is going off, your neighbor John might call you with a certain probability, and your neighbor Mary might call you with a certain probability.
Draw the Bayesian network for this scenario.
Given the following probabilities, what is the probability of there having been an earthquake, given that Mary calls and John does not call?
| P(B←t) | P(B←f) |
|---|---|
| 0.001 | 0.999 |
| P(E←t) | P(E←f) |
|---|---|
| 0.002 | 0.998 |
| B | E | P(A←t | B,E) | P(A←f | B,E) |
|---|---|---|---|
| t | t | 0.95 | 0.05 |
| t | f | 0.94 | 0.06 |
| f | t | 0.29 | 0.71 |
| f | f | 0.001 | 0.999 |
| A | P(J←t | A) | P(J←f | A) |
|---|---|---|
| t | 0.9 | 0.1 |
| f | 0.05 | 0.95 |
| A | P(M←t | A) | P(M←f | A) |
|---|---|---|
| t | 0.7 | 0.3 |
| f | 0.01 | 0.99 |
3. Did the probability of an earthquake (given Mary called) increase because of her call? Or did it go down? Yes or No? And then explain in two sentences why -- use the variables and the dependencies in the network to explain it.