def demo_rejection_sampling():
path_length = 2
jukes_cantor_rate_matrix = RateMatrix.get_jukes_cantor_rate_matrix()
states = 'ACGT'
n = 100000
nielsen_event_count = 0
nielsen_path_count = 0
nielsen_first_time_sum = 0
nielsen_dwell = dict((c, 0) for c in states)
rejection_event_count = 0
rejection_path_count = 0
rejection_first_time_sum = 0
rejection_dwell = dict((c, 0) for c in states)
for i in range(n):
initial_state = 'A'
terminal_state = 'C'
events = get_rejection_sample(initial_state, terminal_state, states, path_length, jukes_cantor_rate_matrix)
if events is not None:
assert events
rejection_path_count += 1
rejection_event_count += len(events)
t, state = events[0]
rejection_first_time_sum += t
extended = [(0, initial_state)] + events + [(path_length, terminal_state)]
for (t0, state0), (t1, state1) in zip(extended[:-1], extended[1:]):
rejection_dwell[state0] += t1 - t0
events = get_nielsen_sample(initial_state, terminal_state, states, path_length, jukes_cantor_rate_matrix)
if events is not None:
assert events
nielsen_path_count += 1
nielsen_event_count += len(events)
t, state = events[0]
nielsen_first_time_sum += t
extended = [(0, initial_state)] + events + [(path_length, terminal_state)]
for (t0, state0), (t1, state1) in zip(extended[:-1], extended[1:]):
nielsen_dwell[state0] += t1 - t0
expected_fraction = RateMatrix.get_jukes_cantor_transition_matrix(path_length)[(initial_state, terminal_state)]
print 'testing the rejection sampling:'
print 'expected fraction:', expected_fraction
print 'observed fraction:', rejection_path_count / float(n)
print 'comparing rejection sampling and nielsen sampling:'
rejection_method_fraction = rejection_event_count / float(rejection_path_count)
nielsen_method_fraction = nielsen_event_count / float(nielsen_path_count)
print 'rejection method fraction:', rejection_method_fraction
print 'nielsen method fraction:', nielsen_method_fraction
print 'comparing time of first event:'
print 'rejection method first event time mean:', rejection_first_time_sum / float(rejection_path_count)
print 'nielsen method first event time mean:', nielsen_first_time_sum / float(nielsen_path_count)
print 'comparing the duration spent in each state:'
print 'rejection:'
for state, t in rejection_dwell.items():
print '\t%s: %f' % (state, t/float(rejection_path_count))
print 'nielsen:'
for state, t in nielsen_dwell.items():
print '\t%s: %f' % (state, t/float(nielsen_path_count))
def test_jukes_cantor_rejection(self):
path_length = 1
jukes_cantor_rate_matrix = RateMatrix.get_jukes_cantor_rate_matrix()
states = 'ACGT'
n = 200
observed = 0
for i in range(n):
events = get_rejection_sample('A', 'C', states, path_length, jukes_cantor_rate_matrix)
if events is not None:
observed += 1
p = RateMatrix.get_jukes_cantor_transition_matrix(path_length)[('A', 'C')]
expected = n*p
variance = n*p*(1-p)
errstr = 'observed: %f expected: %f' % (observed, expected)
self.failUnless(abs(observed - expected) < 3*math.sqrt(variance), errstr)
