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Viterbi once again!

0.9. 0.95. 1:1/6 2:1/6 3:1/6 4:1/6 5:1/6 6:1/6. 1:1/10 2:1/10 3:1/10 4:1/10 5:1/10 6:1/2. 0.05. 0.10. Loaded. Fair. Viterbi once again!. Model generates numbers 312453666641. The unfair casino : Loaded dice p(6) = 0.5; switch fair to load:0.05; switch load to fair: 0.1.

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Viterbi once again!

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  1. 0.9 0.95 1:1/6 2:1/6 3:1/6 4:1/6 5:1/6 6:1/6 1:1/10 2:1/10 3:1/10 4:1/10 5:1/10 6:1/2 0.05 0.10 Loaded Fair Viterbi once again! • Model generates numbers • 312453666641 The unfair casino: Loaded dice p(6) = 0.5; switch fair to load:0.05; switch load to fair: 0.1

  2. Example: 566. What was the series of dice used to generate this output? 0.9 0.95 1:1/6 2:1/6 3:1/6 4:1/6 5:1/6 6:1/6 1:1/10 2:1/10 3:1/10 4:1/10 5:1/10 6:1/2 0.05 0.10 Loaded Fair Model decoding (Viterby) FFF = 0.167*0.95*0.167*0.95*0.167 = 0.0042 FFL = 0.167*0.95*0.167*0.05*0.5 = 0.00666 FLF = 0.167*0.05*0.5*0.1*0.167 = 0.000070 FLL = 0.167*0.05*0.5*0.9*0.5 = 0.0019 LFF LFL LLF LLL

  3. Example: I now add one more say 5! After my first 3 throws I have ended up having either a loaded or a fair dice in my hand The most likely “path” to a loaded dice is FLL = 0.167*0.05*0.5*0.9*0.5 = 0.0019 The most likely path to a fair dice is FFF = 0.167*0.95*0.167*0.95*0.167 = 0.0042 Since the Markov model has no memory, the most likely path to having a fair dice after the 4th through is 0.9 0.95 1:1/6 2:1/6 3:1/6 4:1/6 5:1/6 6:1/6 1:1/10 2:1/10 3:1/10 4:1/10 5:1/10 6:1/2 0.05 0.10 Loaded Fair Model decoding (Viterby)

  4. Log model -0.05 -0.02 1:-0.78 2:-0.78 3:-0.78 4:-0.78 5:-0.78 6:-0-78 1:-1 2:-1 3:-1 4:-1 5:-1 6:-0.3 -1.3 -1 Fair Loaded Model decoding (Viterby)

  5. Log model -0.05 -0.02 1:-0.78 2:-0.78 3:-0.78 4:-0.78 5:-0.78 6:-0-78 1:-1 2:-1 3:-1 4:-1 5:-1 6:-0.3 -1.3 -1 Fair Loaded Model decoding (Viterby) Identify what series of dice was used to generate this output?

  6. Log model -0.05 -0.02 1:-0.78 2:-0.78 3:-0.78 4:-0.78 5:-0.78 6:-0-78 1:-1 2:-1 3:-1 4:-1 5:-1 6:-0.3 -1.3 -1 Fair Loaded Model decoding (Viterby) Series of dice is FFFFLLL

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