Using the model from file:  coins1.json  - You can modify the parameters A, B and pi in this file to build different HMM models
Observations =  ('Heads', 'Heads', 'Heads')  Fwd Prob =  0.14534  Bwd Prob =  0.14534  total_1 =  0.14534  total_2 =  0.14534
Observations =  ('Heads', 'Heads', 'Tails')  Fwd Prob =  0.12906  Bwd Prob =  0.12906  total_1 =  0.2744  total_2 =  0.2744
Observations =  ('Heads', 'Tails', 'Heads')  Fwd Prob =  0.12158  Bwd Prob =  0.12158  total_1 =  0.39598  total_2 =  0.39598
Observations =  ('Heads', 'Tails', 'Tails')  Fwd Prob =  0.12402  Bwd Prob =  0.12402  total_1 =  0.52  total_2 =  0.52
Observations =  ('Tails', 'Heads', 'Heads')  Fwd Prob =  0.1239  Bwd Prob =  0.1239  total_1 =  0.6439  total_2 =  0.6439
Observations =  ('Tails', 'Heads', 'Tails')  Fwd Prob =  0.1137  Bwd Prob =  0.1137  total_1 =  0.7576  total_2 =  0.7576
Observations =  ('Tails', 'Tails', 'Heads')  Fwd Prob =  0.11838  Bwd Prob =  0.11838  total_1 =  0.87598  total_2 =  0.87598
Observations =  ('Tails', 'Tails', 'Tails')  Fwd Prob =  0.12402  Bwd Prob =  0.12402  total_1 =  1.0  total_2 =  1.0
Max Probability =  2.42167160869e-07  Hidden State Sequence =  [u'Coin 2', u'Coin 2', u'Coin 1', u'Coin 1', u'Coin 1', u'Coin 1', u'Coin 2', u'Coin 2', u'Coin 2', u'Coin 1', u'Coin 1', u'Coin 2']
Learning the model through Forward-Backward Algorithm for the observations ('Tails', 'Tails', 'Heads', 'Heads', 'Heads', 'Heads', 'Tails', 'Tails', 'Tails', 'Heads', 'Heads', 'Tails')
Using the model from file:  random1.json  - You can modify the parameters A, B and pi in this file to build different HMM models
The new model parameters after 1 iteration are:
A =  {u'Coin 1': {u'Coin 1': 0.09395581590221148, u'Coin 3': 0.6413323522659057, u'Coin 2': 0.26471183183188296}, u'Coin 3': {u'Coin 1': 0.27219717693130485, u'Coin 3': 0.3965284515987993, u'Coin 2': 0.3312743714698958}, u'Coin 2': {u'Coin 1': 0.7631066838408123, u'Coin 3': 0.09105435757132309, u'Coin 2': 0.14583895858786486}}
B =  {u'Coin 1': {u'Tails': 0.7045611480940691, u'Heads': 0.2954388519059312}, u'Coin 3': {u'Tails': 0.36370548397177777, u'Heads': 0.6362945160282223}, u'Coin 2': {u'Tails': 0.4274817845151278, u'Heads': 0.5725182154848724}}
pi =  {u'Coin 1': 0.3549567578486951, u'Coin 3': 0.2664022397385963, u'Coin 2': 0.3786410024127086}