Download Decision Trees

How to construct a decision tree
1.
2.
3.
4.
5.
6.
List each decision nodes & its alternatives.
List each chances nodes& its alternatives.
Draw the nodes and links.
Add costs & probabilities along links
Calculate utilities for utility (leftmost) nodes
Calculate expected utilities
Example
• You need to decide whether to do a fancy project or
a mundane project. Either project can succeed or
fail. There is a 10% chance of success for the fancy
project, and 80% chance of success for the mundane
project. The fancy project costs 1M$ to execute, and
if it succeeds, you get 11M$. If you lose, you get
nothing. The mundane project costs 0.5M$ to
execute, and you get 1.5M$ if it succeeds. If it fails,
you get nothing. Which project should you do?
1. List each decision nodes & its alternatives.
•
Which project?
–
–
Fancy
Mundane
You need to decide whether to do a fancy project or a
mundane project. Either project can succeed or fail. There
is a 10% chance of success for the fancy project, and 80%
chance of success for the mundane project. The fancy
project costs 1M$ to execute, and if it succeeds, you get
11M$. If you lose, you get nothing. The mundane project
costs 0.5M$ to execute, and you get 1.5M$ if it succeeds.
If it fails, you get nothing. Which project should you do?
2. List each chance nodes & its alternatives.
•
Outcome?
–
–
Success
Failure
You need to decide whether to do a fancy project or a
mundane project. Either project can succeed or fail. There
is a 10% chance of success for the fancy project, and 80%
chance of success for the mundane project. The fancy
project costs 1M$ to execute, and if it succeeds, you get
11M$. If you lose, you get nothing. The mundane project
costs 0.5M$ to execute, and you get 1.5M$ if it succeeds.
If it fails, you get nothing. Which project should you do?
3. Draw nodes as tree
You need to decide whether to do a
fancy project or a mundane project.
Either project can succeed or fail.
There is a 10% chance of success for
the fancy project, and 80% chance of
success for the mundane project.
The fancy project costs 1M$ to
execute, and if it succeeds, you get
11M$. If you lose, you get nothing.
The mundane project costs 0.5M$ to
execute, and you get 1.5M$ if it
succeeds. If it fails, you get nothing.
Which project should you do?
Outcome?
Project?
Outcome?
Decision
nodes
are
square
Chance
nodes
are oval
Utility
nodes are
like
diamonds
4. Add costs and probabilities to
links
You need to decide whether to do a
fancy project or a mundane project.
Either project can succeed or fail.
There is a 10% chance of success for
the fancy project, and 80% chance of
success for the mundane project.
The fancy project costs 1M$ to
execute, and if it succeeds, you get
11M$. If you lose, you get nothing.
The mundane project costs 0.5M$ to
execute, and you get 1.5M$ if it
succeeds. If it fails, you get nothing.
Which project should you do?
Outcome?
Project?
Outcome?
5. Calculate utility values for utility nodes
You need to decide whether to do a
fancy project or a mundane project.
Either project can succeed or fail.
There is a 10% chance of success for
the fancy project, and 80% chance of
success for the mundane project.
The fancy project costs 1M$ to
execute, and if it succeeds, you get
11M$. If you lose, you get nothing.
The mundane project costs 0.5M$ to
execute, and you get 1.5M$ if it
succeeds. If it fails, you get nothing.
Which project should you do?
10M$
Benefit: 11M$
Cost: 1M$
Outcome?
-1M$
Project?
1M$
Outcome?
-0.5M$
Benefit: 0
Cost: 0.5M$
6. Calculate expected utilities, moving leftward
You need to decide whether to do a
fancy project or a mundane project.
Either project can succeed or fail.
There is a 10% chance of success for
the fancy project, and 80% chance of
success for the mundane project.
The fancy project costs 1M$ to
execute, and if it succeeds, you get
11M$. If you lose, you get nothing.
The mundane project costs 0.5M$ to
execute, and you get 1.5M$ if it
succeeds. If it fails, you get nothing.
Which project should you do?
EU = 0.1*10=1.0
10M$
Outcome?
EU = 0.9*(-1)=-0.9
-1M$
Project?
EU = 0.8*1=0.8
1M$
Outcome?
EU = 0.2*(-0.5)=-0.1
-0.5M$
6. Calculate expected utilities moving leftward
You need to decide whether to do a
fancy project or a mundane project.
Either project can succeed or fail.
There is a 10% chance of success for
the fancy project, and 80% chance of
success for the mundane project.
The fancy project costs 1M$ to
execute, and if it succeeds, you get
11M$. If you lose, you get nothing.
The mundane project costs 0.5M$ to
execute, and you get 1.5M$ if it
succeeds. If it fails, you get nothing.
Which project should you do?
EU = 1.0-0.9= 0.1
EU = 0.1*10=1.0
10M$
Outcome?
EU = 0.9*(-1)=-0.9
-1M$
Project?
EU = 0.8-0.1=0.7
EU = 0.8*1=0.8
1M$
Outcome?
EU = 0.2*(-0.5)=-0.1
-0.5M$
6. Calculate expected utilities moving leftward
You need to decide whether to do a
fancy project or a mundane project.
Either project can succeed or fail.
There is a 10% chance of success for
the fancy project, and 80% chance of
success for the mundane project.
The fancy project costs 1M$ to
execute, and if it succeeds, you get
11M$. If you lose, you get nothing.
The mundane project costs 0.5M$ to
execute, and you get 1.5M$ if it
succeeds. If it fails, you get nothing.
Which project should you do?
EU = 1.0-0.9= 0.1
EU = 0.1*10=1.0
10M$
Outcome?
EU = 0.9*(-1)=-0.9
-1M$
Project?
EU = 0.8-0.1=0.7
EU = 0.8*1=0.8
1M$
Outcome?
Best choice
EU = 0.2*(-0.5)=-0.1
-0.5M$
A more complex example
• Your show dog has cancer. If you do nothing, there is a
90% chance she will die. If she has surgery, there is a
40% chance of curing the cancer, 10% chance of dying
from the surgery, and a 50% chance that the cancer will
survive, in which case, she has the usual 90% chance of
dying. If she gets chemo, there is a 20% chance of
curing the cancer, and an 80% that the cancer will
remain, in which surgery can be performed, with the
same risks and outcomes as mentioned above. Chemo
cannot be done after surgery, by the way. The dog is
worth 900K$ if she is alive, and nothing if she is dead.
Surgery costs $10K and chemo costs 4K$. What should
you do?
1. List each decision nodes & its alternatives.
•
Which treatment?
–
–
–
•
surgery
chemo
Nothing
After chemo fails, which treatment?
–
–
surgery
nothing
Your show dog has cancer. If you do nothing, there is a 90% chance she
will die. If she has surgery, there is a 40% chance of curing the cancer,
10% chance of dying from the surgery, and a 50% chance that the cancer
will survive, in which case, she has the usual 90% chance of dying. If she
gets chemo, there is a 20% chance of curing the cancer, and an 80% that
the cancer will remain, in which surgery can be performed, with the same
risks and outcomes as mentioned above. Chemo cannot be done after
surgery, by the way. The dog is worth 900K$ if she is alive, and nothing if
she is dead. Surgery costs $10K and chemo costs 4K$. What should you
do?
2. List each chance nodes & its alternatives.
•
Outcome?
–
–
–
Cancer cured
Died due to surgery (only for surgery node)
Cancer not cured
Your show dog has cancer. If you do nothing, there is a 90% chance she will
die. If she has surgery, there is a 40% chance of curing the cancer, 10%
chance of dying from the surgery, and a 50% chance that the cancer will
survive, in which case, she has the usual 90% chance of dying. If she gets
chemo, there is a 20% chance of curing the cancer, and an 80% that the
cancer will remain, in which surgery can be performed, with the same risks and
outcomes as mentioned above. Chemo cannot be done after surgery, by the
way. The dog is worth 900K$ if she is alive, and nothing if she is dead.
Surgery costs $10K and chemo costs 4K$. What should you do?
3. Draw nodes
•Your show dog has cancer. If you do nothing,
there is a 90% chance she will die. If she has
surgery, there is a 40% chance of curing the
cancer, 10% chance of dying from the surgery,
and a 50% chance that the cancer will survive, in
which case, she has the usual 90% chance of
dying. If she gets chemo, there is a 20% chance
of curing the cancer, and an 80% that the cancer
will remain, in which surgery can be performed,
with the same risks and outcomes as mentioned
above. Chemo cannot be done after surgery, by
the way. The dog is worth 900K$ if she is alive,
and nothing if she is dead. Surgery costs $10K
and chemo costs 4K$. What should you do?
Outcome?
uncured
Die?
Treatment?
Outcome?
Outcome?
Treatment?
Nothing
Outcome?
Die?
4. Add costs & probabilities
•Your show dog has cancer. If you do nothing,
there is a 90% chance she will die. If she has
surgery, there is a 40% chance of curing the
cancer, 10% chance of dying from the surgery,
and a 50% chance that the cancer will survive, in
which case, she has the usual 90% chance of
dying. If she gets chemo, there is a 20% chance
of curing the cancer, and an 80% that the cancer
will remain, in which surgery can be performed,
with the same risks and outcomes as mentioned
above. Chemo cannot be done after surgery, by
the way. The dog is worth 900K$ if she is alive,
and nothing if she is dead. Surgery costs $10K
and chemo costs 4K$. What should you do?
Outcome?
uncured
p=0.5
Die?
Treatment?
Outcome?
Outcome?
Treatment?
Nothing
Outcome?
Die?
5. Calculate utility values for utility nodes
•Your show dog has cancer. If you do nothing,
there is a 90% chance she will die. If she has
surgery, there is a 40% chance of curing the
cancer, 10% chance of dying from the surgery,
and a 50% chance that the cancer will survive, in
which case, she has the usual 90% chance of
dying. If she gets chemo, there is a 20% chance
of curing the cancer, and an 80% that the cancer
will remain, in which surgery can be performed,
with the same risks and outcomes as mentioned
above. Chemo cannot be done after surgery, by
the way. The dog is worth 900K$ if she is alive,
and nothing if she is dead. Surgery costs $10K
and chemo costs 4K$. What should you do?
890K$
-10K$
Outcome?
uncured
p=0.5
Die?
890K$
-10K$
Treatment?
896K$
Outcome?
Outcome?
0$
Outcome?
900K$
Treatment?
Nothing
Die?
-4K$
896K$
6. Calculate expected utilities
•Your show dog has cancer. If you do nothing,
there is a 90% chance she will die. If she has
surgery, there is a 40% chance of curing the
cancer, 10% chance of dying from the surgery,
and a 50% chance that the cancer will survive, in
which case, she has the usual 90% chance of
dying. If she gets chemo, there is a 20% chance
of curing the cancer, and an 80% that the cancer
will remain, in which surgery can be performed,
with the same risks and outcomes as mentioned
above. Chemo cannot be done after surgery, by
the way. The dog is worth 900K$ if she is alive,
and nothing if she is dead. Surgery costs $10K
and chemo costs 4K$. What should you do?
890K$
-10K$
Outcome?
uncured
p=0.5
EU=80
Die?
890K$
-10K$
Treatment?
896K$
Outcome?
Outcome?
0$
Outcome?
900K$
Treatment?
Nothing
EU=86
Die?
-4K$
896K$
My disk drive is flakey. Tech says that there is
a 10% chance it will crash in the next week,
and replacing the disk and data will cost me
$200. If I replace the disk, it will cost me $70
and it will not crash. If I save its contents to
DVD, reformat and restore it, then it costs me
4 hours (equivalent to $40) but reduces the
chance of crashing to 3%.
EU = 0.03*(-240)+0.97*(-40) = -46
-240
Crash?
-40
Save,
reformat,
restore?
-200
Replace
disk?
Crash?
0
-70
EU = 0.10*(-200)+0.90*(0) = -20
EU = -70
Quiz question
• You will be drilling a water well in your backyard, and
you have to decide where to dig it. If you just dig
where you think it is best, there is a 40% chance you’ll
hit water. If you hire a seismologist, the chances
increase to 60% but it costs you 10K$. If you hire a
water witch, the chance of hitting water is 50% and the
cost is 1K$. If you get 50K$ for hitting water, what
should you do
• Draw the decision tree
• Evaluate alternatives
• Indicate best choice
• Put your name on the paper and hand it in.
You will be drilling a water well in your backyard,
and you have to decide where to dig it. If you just
dig where you think it is best, there is a 40%
chance you’ll hit water. If you hire a seismologist,
the chances increase to 60% but it costs you 10K$.
If you hire a water witch, the chance of hitting
water is 50% and the cost is 1K$. If you get 50K$
for hitting water, what should you do?
49K$
Water?
-1K$
40K$
Detector?
Seismologist
Cost 10K
EU=20
Water?
50K$
Water?
0
-10K$