from lea import __version__, event, if_, joint, P
print ("Using Lea",__version__)

cold    = event(0.200)
flu     = event(0.100)
covid19 = event(0.005)
print ("OK (prior probabilities set)")

P(cold)

fever_if_sole_cold    = event(0.4)
fever_if_sole_flu     = event(0.8)
fever_if_sole_covid19 = event(0.9)
print ("OK (fever conditional probabilities set)")

cough_if_sole_cold    = event(0.8)
cough_if_sole_flu     = event(0.2)
cough_if_sole_covid19 = event(0.6)
print ("OK (cough conditional probabilities set)")

fever_by_cold    = if_(cold   , fever_if_sole_cold   , False)
fever_by_flu     = if_(flu    , fever_if_sole_flu    , False)
fever_by_covid19 = if_(covid19, fever_if_sole_covid19, False)
cough_by_cold    = if_(cold   , cough_if_sole_cold   , False)
cough_by_flu     = if_(flu    , cough_if_sole_flu    , False)
cough_by_covid19 = if_(covid19, cough_if_sole_covid19, False)
fever = fever_by_cold | fever_by_flu | fever_by_covid19
cough = cough_by_cold | cough_by_flu | cough_by_covid19
print ("OK (probabilistic model set up)")

P(fever)

P(covid19.given(fever))

P(covid19.given(fever,cough))

P(covid19.given(fever,~cough))

P(covid19.given(~fever,~cough))

P(flu.given(fever,cough))

P(covid19.given(fever,cough,~cold))

P(covid19.given(fever,cough,~cold,~flu))

joint(fever,cough)

joint(covid19,fever,cough)

joint(fever,cough).given(covid19)

symptom = fever | cough
print ("OK (symptom defined)")

P(symptom.given(covid19))

P(symptom.given(~covid19))

death = if_(covid19, event(0.034), event(0.0002))
print ("OK (death defined)")

P(death.given(fever,cough))

P(covid19.given(death))

P(covid19.given(death,~symptom))

joint(covid19,symptom).given(death)

c = event(0.034)
a_lt_65_if_c = event(0.19)
a_lt_65_prior = event(0.92)
a_lt_65 = if_(c, a_lt_65_if_c, prior_lea=a_lt_65_prior)
print ("OK (model defined)")

P(c.given(a_lt_65))

c = event('c')
a_lt_65_if_c = event('a')
a_lt_65_prior = event('b')
a_lt_65 = if_(c, a_lt_65_if_c, prior_lea=a_lt_65_prior)
print ("OK (symbolic model defined)")

P(c.given(a_lt_65))

P(a_lt_65.given(~c))

joint(c,a_lt_65)