Viterbi once again! Model generates numbers –312453666641 1:1/6 2:1/6 3:1/6 4:1/6 5:1/6 6:1/6 Fair 1:1/10 2:1/10 3:1/10 4:1/10 5:1/10 6:1/2 Loaded 0.95.

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Presentation transcript:

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

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

Model decoding (Viterby) 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 = The most likely path to a fair dice is FFF = 0.167*0.95*0.167*0.95*0.167 = Since the Markov model has no memory, the most likely path to having a fair dice after the 4th through is 1:1/6 2:1/6 3:1/6 4:1/6 5:1/6 6:1/6 Fair 1:1/10 2:1/10 3:1/10 4:1/10 5:1/10 6:1/2 Loaded

Model decoding (Viterby) 1: : : : : :-0-78 Fair 1:-1 2:-1 3:-1 4:-1 5:-1 6:-0.3 Loaded Log model F L Null

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

Model decoding (Viterby) 1: : : : : :-0-78 Fair 1:-1 2:-1 3:-1 4:-1 5:-1 6:-0.3 Loaded Log model F L Null Series of dice is FFFFLLL