Archive for SAMSI

sudoku break

Posted in pictures, R, Statistics with tags , , , , on December 13, 2013 by xi'an

sudo291113While in Warwick last week, one evening after having exhausted my laptop battery, I tried the following Sudoku (from Libération):

>   printSudoku(readSudoku("libe.dk"))
  +-------+-------+-------+
  | 4   6 |   2   | 3   9 |
  |   3   |       |   2   |
  | 7   2 |       | 5   6 |
  +-------+-------+-------+
  |       | 9 4 5 |       |
  | 5     | 7 6 2 |     1 |
  |       | 3 1 8 |       |
  +-------+-------+-------+
  | 6   9 |       | 1   3 |
  |   7   |       |   9   |
  | 3   1 |   9   | 4   7 |
  +-------+-------+-------+

and could not even start. As it happened, this was a setting with no deterministic move, i.e. all free/empty entries had multiple possible values. So after trying for a while and following trees to no obvious contradiction (!) I decided to give up and on the next day (with power) to call my “old” sudoku solver (built while at SAMSI), using simulated annealing and got the result after a few thousand iterations. The detail of the exploration is represented above, the two colours being code for two different moves on the Sudoku table. Leading to the solution

  +-------+-------+-------+
  | 4 8 6 | 5 2 1 | 3 7 9 |
  | 1 3 5 | 6 7 9 | 8 2 4 |
  | 7 9 2 | 8 3 4 | 5 1 6 |
  +-------+-------+-------+
  | 2 1 3 | 9 4 5 | 7 6 8 |
  | 5 4 8 | 7 6 2 | 9 3 1 |
  | 9 6 7 | 3 1 8 | 2 4 5 |
  +-------+-------+-------+
  | 6 2 9 | 4 8 7 | 1 5 3 |
  | 8 7 4 | 1 5 3 | 6 9 2 |
  | 3 5 1 | 2 9 6 | 4 8 7 |
  +-------+-------+-------+

I then tried a variant with more proposals (hence more colours) at each iteration, which ended up being stuck at a penalty of 4 (instead of 0) in the final thousand iterations. Although this is a one occurrence experiment, I find it interesting that having move proposals may get the algorithm stuck faster in a local minimum. Nothing very deep there, of course..!

sudo301113

SAMSI workshop

Posted in Statistics, Travel with tags , , , , on March 22, 2010 by xi'an

Taking advantage of the people gathered at Frontiers of Statistical Decision Making and Bayesian Analysis, Dongchu Sun organised a one-day SAMSI workshop on reference priors for spatio-temporal models. Talking with a small group focused on this  topic was quite enjoyable and a change from the larger crowds at the conference (even though talks were also enjoyable there!). I particularly appreciated the discussion we had around AR(p) models and the difficulty of assessing whether or not non-stationary regions should be included in the analysis. The generalisation of the Berger-Yang (1994) paradigm to general values of p seems to put too much mass on the non-stationary region, even when using a symmetrisation technique… I came out of the meeting (exhausted and) wondering whether or not it was at all meaningfull to consider testing for stationarity, even though Bayes factors can be constructed in this setting.