Admistrivia

• Midterms look great!
• Read p 215 - 223.

Models

Double stochastic

• Row sums and column sums are both 1
• What is the stationary distribution? Uniform!
• Generalization of "reversable"
• All of physics is reversable
• Hence: the world will evolve to a uniform distribution
• Strong links to 2nd law of thermodynamics

2 step Markov instead of 1 step

• Build in history
• Simple model of depression: Happy, Sad.
• If "sad" twice in row, much more likely to be "sad" following time.
• We could call this a new name "depressed".
• Fraction happy is (H,S) + (H,H). NOTE: this is the same as (H,H) + (H,S).

Sampling plans

• Two manufacturing policies:
  • cross fingers and hope for the best
  • sample every item and fix those that are broken
• Each has its advantages
• But, doing the wrong one is an expensive mistake
• How about we dynamically switch back an forth?
• Model:
  • Each item has probability p of being defective
  • We will switch from sampling at rate 1/r, to complete sampling.
  • One defective --> switch to complete sampling
  • k nondefectives --> switch to random sampling
  • What does the limiting behavior look like?
  • Sampling increase as defects increase
  • Maximum error rate is bounded
  • All can be exactly computed (see page 218-220)