In a Hidden-Markov Model where there is fair die
and a loaded die (with Prob(head)=1/3, Prob(Tail)=2/3)
and the outcome was, 10, Heads and , 10, tails
The most reasonable(Bayesian-Laplace style not ML) estimate
for the probability of using the fair die is
2863343001597125
----------------
4873041614471168
that in floating point is, 0.5875884567
In a Hidden-Markov Model where there is fair die
and a loaded die (with Prob(head)=1/3, Prob(Tail)=2/3)
and the outcome was, 20, Heads and , 20, tails
The most reasonable(Bayesian-Laplace style not ML) estimate
for the probability of using the fair die is
327381605443283609260043381137
------------------------------
500237630717560914135201349632
that in floating point is, 0.6544521750
In a Hidden-Markov Model where there is fair die
and a loaded die (with Prob(head)=1/3, Prob(Tail)=2/3)
and the outcome was, 30, Heads and , 30, tails
The most reasonable(Bayesian-Laplace style not ML) estimate
for the probability of using the fair die is
12792251351728996089211427953540765767352372363
-----------------------------------------------
18197283968799193634658020753335072511875874816
that in floating point is, 0.7029758602
In a Hidden-Markov Model where there is fair die
and a loaded die (with Prob(head)=1/3, Prob(Tail)=2/3)
and the outcome was, 40, Heads and , 40, tails
The most reasonable(Bayesian-Laplace style not ML) estimate
for the probability of using the fair die is
197442711694271771810537484166464324867464893948112053755137411
---------------------------------------------------------------
267513351741818722858367094244055284106004524619103095033430016
that in floating point is, 0.7380667560
In a Hidden-Markov Model where there is fair die
and a loaded die (with Prob(head)=1/3, Prob(Tail)=2/3)
and the outcome was, 50, Heads and , 50, tails
The most reasonable(Bayesian-Laplace style not ML) estimate
for the probability of using the fair die is
179971448156000456555254178467389100643966216843242522316883872508528795235
/
/
/
235556526962676761530958292908591768503738161606911513989651378226904170496
that in floating point is, 0.7640265820
This took, 29.037, seconds