Assignments for Friday:

• Think about questions you want to discuss on Friday
• What is the difference/similarity between Bayesian posterior probability and Bootstrap support?
• Read about dN and dS (example: page 240/241 in text book, or here, here and here)
  

   

dN/dS slides

return quiz 7, discuss quiz 8

McRobot is here ;

Install and start the program (double click on the icon):

Press <CTRL> and the o key simultaneously - this opens the options window

Uncheck "Robot ignores topography"

Check "Allow Rotation"

Click Ok

Click and drag in the application window to create a few hills

CTRL f starts a robot running around in the landscape

CTRL n lets the robot continue a trajectory

(CTRL t turns on/off the trajectory. If off, you only see the points where the robot lands to make a new decision)

Right Click drag allows you to look at the landscape you created from the side.

Place two hills in the Landscape, one much larger than the other.

CTRLf   CTRL n CTRL n CTRL n CTRL n CTRL n CTRL n CTRL n

Notice that the Robot tends to be trapped on one hill and has difficulty to switch from one hill to the other. Sadly, Metropolis and Hastings say that you need to run the robot for an indefinite amount of time for the frequency to approach the posterior probability. When has on run the robot long enough to approach infinity? How to decide, if one doesn't know the landscape?
One solution to facilitate the exploration of the landscape is to send out scouts, aka heated chains. These are robots that follow the same rules but see a landscape that is melted down. After each step the chains compare their posterior probability and if the scout is in a better place they switch.

Using the same landscape, select 4 chains in the chains menu.

CTRLf   CTRL n CTRL n CTRL n CTRL n CTRL n CTRL n CTRL n

The robot (blue chain) should switch frequently between hills.

To see the heated chains in their landscapes, select "all chains" in the Show- menu

CTRL t to toggle on/off the trajectory display

Because you placed the probability hills in the landscape, you can compare the frequency with which the robot is found in an area with the probability (select summarize in the show menu). The longer you run the the robot, the more precise your probability estimate becomes. (Same for bootstrap, the more samples the more precise (i.e. reproducible) the probability estimate; in both cases the problem is that, if you have a systematic error (compositional bias, long branch attraction), all the precision in the world will not catch the error.)