def coal_mining_desaster(modelname='pymc3_coal_mining_disaster_model'):
"""TODO: Documentation here. why is there two returned models? what for?"""
# data
disasters = np.array([
4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6, 3, 3, 5, 4, 5, 3, 1, 4,
4, 1, 5, 5, 3, 4, 2, 5, 2, 2, 3, 4, 2, 1, 3, 3, 2, 1, 1, 1, 1, 3, 0, 0,
1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 2,
1, 0, 0, 0, 1, 1, 0, 2, 3, 3, 1, 2, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,
0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1
])
years = np.arange(1851, 1962)
data = pd.DataFrame({'years': years, 'disasters': disasters})
years = theano.shared(years)
with pm.Model() as disaster_model:
switchpoint = pm.DiscreteUniform('switchpoint',
lower=years.min(),
upper=years.max(),
testval=1900)
# Priors for pre- and post-switch rates number of disasters
early_rate = pm.Exponential('early_rate', 1.0)
late_rate = pm.Exponential('late_rate', 1.0)
# Allocate appropriate Poisson rates to years before and after current
rate = pm.math.switch(switchpoint >= years, early_rate, late_rate)
disasters = pm.Poisson('disasters', rate, observed=data['disasters'])
# years = pm.Normal('years', mu=data['years'], sd=0.1, observed=data['years'])
model = ProbabilisticPymc3Model(modelname,
disaster_model,
shared_vars={'years': years})
model_fitted = model.copy(name=modelname + '_fitted').fit(data)
return model, model_fitted
def create_pymc3_getting_started_model(modelname='pymc3_getting_started_model',
fit=True):
if fit:
modelname = modelname + '_fitted'
np.random.seed(123)
alpha, sigma = 1, 1
beta_0 = 1
beta_1 = 2.5
size = 100
X1 = np.random.randn(size)
X2 = np.random.randn(size) * 0.2
Y = alpha + beta_0 * X1 + beta_1 * X2 + np.random.randn(size) * sigma
data = pd.DataFrame({'X1': X1, 'X2': X2, 'Y': Y})
basic_model = pm.Model()
with basic_model:
# Priors for unknown model parameters
alpha = pm.Normal('alpha', mu=0, sd=10)
beta_0 = pm.Normal('beta_0', mu=0, sd=10)
beta_1 = pm.Normal('beta_1', mu=0, sd=10)
sigma = pm.HalfNormal('sigma', sd=5)
# Expected value of outcome
mu = alpha + beta_0 * data['X1'] + beta_1 * data['X2']
# Likelihood (sampling distribution) of observations
Y = pm.Normal('Y', mu=mu, sd=sigma, observed=data['Y'])
X1 = pm.Normal('X1', mu=data['X1'], sd=sigma, observed=data['X1'])
X2 = pm.Normal('X2', mu=data['X2'], sd=sigma, observed=data['X2'])
m = ProbabilisticPymc3Model(modelname, basic_model)
if fit:
m.fit(data)
return data, m
def create_allbus_model_5(filename='test_allbus.csv',
modelname='allbus_model_5',
fit=True):
if fit:
modelname = modelname + '_fitted'
# Load and prepare data
data = pd.read_csv(filename, index_col=0)
data = data.drop(
['eastwest', 'lived_abroad', 'spectrum', 'sex', 'educ', 'health'],
axis=1)
# Reduce size of data to improve performance
data = data.sample(n=500, random_state=1)
data.sort_index(inplace=True)
# Set up shared variables
age = theano.shared(np.array(data['age']))
allbus_model = pm.Model()
with allbus_model:
# priors
alpha_sd = pm.Uniform('alpha_sd', 0, 2000)
beta_sd = pm.Uniform('beta_sd', 0, 1000)
loc_transform = pm.Normal('loc_transform', 50, 20)
scale_transform = pm.Uniform('scale_transform', 0, 100)
sd_happ = pm.Uniform('sd_happ', 0, 5)
k_logistic = pm.Uniform('k_logistic', 0, 10)
x_0_logistic = pm.Uniform('x_0_logistic', 0, 1000)
# likelihood
# transform age so that it resembles a bell-shaped distribution
def normal_pdf(x, loc, scale):
return 1 / np.sqrt(2 * math.pi * scale**2) * np.exp(-(x - loc)**2 /
(2 * scale**2))
age_transformed = normal_pdf(age,
loc=loc_transform,
scale=scale_transform)
sd_income = alpha_sd + beta_sd * age_transformed
age + loc_transform
income = pm.HalfNormal('income', sd_income, observed=data['income'])
def logistic_func(l, k, x, x_0):
# l: curve's max value
# x_0: x_value of sigmoid's mid-point
# k: steepness of the curve
return l / (1 + np.exp(-k * (x - x_0)))
mu_happ = logistic_func(10, k_logistic, income, x_0_logistic)
happiness = pm.Normal('happiness',
mu_happ,
sd_happ,
observed=data['happiness'])
# Create model instance for Lumen
m = ProbabilisticPymc3Model(modelname,
allbus_model,
shared_vars={'age': age})
if fit:
m.fit(data)
return data, m
def create_allbus_model_4(filename='test_allbus.csv',
modelname='allbus_model_4',
fit=True):
if fit:
modelname = modelname + '_fitted'
# Load and prepare data
data = pd.read_csv(filename, index_col=0)
data = data.drop(
['eastwest', 'lived_abroad', 'spectrum', 'sex', 'educ', 'health'],
axis=1)
# Reduce size of data to improve performance
data = data.sample(n=500, random_state=1)
data.sort_index(inplace=True)
# Set up shared variables
age = theano.shared(np.array(data['age']))
allbus_model = pm.Model()
with allbus_model:
# priors
alpha_sd = pm.Uniform('alpha_sd', 0, 2000)
beta_sd = pm.Uniform('beta_sd', 0, 1000)
loc_transform = pm.Normal('loc_transform', 50, 20)
scale_transform = pm.Uniform('scale_transform', 0, 100)
sd_happ = pm.Uniform('sd_happ', 0, 5)
alpha_happ1 = pm.Uniform('alpha_happ1', -10, 5)
alpha_happ2 = pm.Uniform('alpha_happ2', 5, 10)
beta_happ1 = pm.Uniform('beta_happ1', -0.001, 0.001)
beta_happ2 = pm.Uniform('beta_happ2', -0.001, 0.001)
# likelihood
# transform age so that it resembles a bell-shaped distribution
def normal_pdf(x, loc, scale):
return 1 / np.sqrt(2 * math.pi * scale * scale) * np.exp(
-(x - loc)**2 / (2 * scale * scale))
age_transformed = normal_pdf(age,
loc=loc_transform,
scale=scale_transform)
sd_income = alpha_sd + beta_sd * age_transformed
income = pm.HalfNormal('income', sd_income, observed=data['income'])
switchpoint = pm.Uniform('switchpoint', 500, 2000)
beta_happ = pm.math.switch(income < switchpoint, beta_happ1,
beta_happ2)
alpha_happ = pm.math.switch(income < switchpoint, alpha_happ1,
alpha_happ2)
mu_happ = alpha_happ + beta_happ * income
# Cap happiness at 10
mu_happ = pm.math.switch(mu_happ < 10, mu_happ, 10)
happiness = pm.Normal('happiness',
mu_happ,
sd_happ,
observed=data['happiness'])
# Create model instance for Lumen
m = ProbabilisticPymc3Model(modelname,
allbus_model,
shared_vars={'age': age})
if fit:
m.fit(data)
return data, m
def create_flight_delay_model_2(filename='airlineDelayDataProcessed.csv',
modelname='flight_delay_2',
fit=True):
if fit:
modelname = modelname + '_fitted'
data = pd.read_csv(filename)
data = data.rename(columns={
'DEP_TIME': 'dep_time',
'DEP_DELAY': 'depdelay'
})
# Drop variables that are not considered in the model
data = data.drop([
'UNIQUE_CARRIER', 'DAY_OF_MONTH', 'DAY_OF_WEEK', 'ORIGIN_AIRPORT_ID',
'DEST_AIRPORT_ID', 'ACTUAL_ELAPSED_TIME', 'ARR_DELAY', 'DISTANCE'
],
axis=1)
# Reduce size of data to improve performance
data = data.sample(n=1000, random_state=1)
data.sort_index(inplace=True)
# Create shared variables
deptime = theano.shared(np.array(data['dep_time']))
# Create model
delay_model = pm.Model()
with delay_model:
beta_dep = pm.Uniform('beta_dep', 0, 1, shape=2)
beta_var = pm.Uniform('beta_var', 0, 1, shape=2)
# Improvement 1: Assume that variance is a linear function of time, instead of uniformly distributed
var = beta_var[0] + beta_var[1] * deptime
# I assume that depdelay is a function of deptime
mu_depdelay = beta_dep[0] + beta_dep[1] * deptime
depdelay = pm.Normal('depdelay',
mu_depdelay,
var,
observed=data['depdelay'])
m = ProbabilisticPymc3Model(modelname,
delay_model,
shared_vars={'dep_time': deptime})
if fit:
m.fit(data)
return data, m
def create_allbus_model_1(filename='test_allbus.csv',
modelname='allbus_model_1',
fit=True):
if fit:
modelname = modelname + '_fitted'
# Load and prepare data
data = pd.read_csv(filename, index_col=0)
data = data.drop(
['eastwest', 'lived_abroad', 'spectrum', 'sex', 'educ', 'health'],
axis=1)
# Reduce size of data to improve performance
data = data.sample(n=500, random_state=1)
data.sort_index(inplace=True)
# Set up shared variables
age = theano.shared(np.array(data['age']))
allbus_model = pm.Model()
with allbus_model:
# priors
sd_income = pm.Uniform('sd_income', 0, 1000)
alpha_inc = pm.Uniform('alpha_inc', -1000, 1000)
beta_inc = pm.Uniform('beta_inc', -100, 100)
sd_happ = pm.Uniform('sd_happ', 0, 5)
alpha_happ = pm.Uniform('alpha_happ', -10, 10)
beta_happ = pm.Uniform('beta_happ', -0.001, 0.001)
# likelihood
mu_income = alpha_inc + beta_inc * age
income = pm.Normal('income',
mu_income,
sd_income,
observed=data['income'])
mu_happ = alpha_happ + beta_happ * income
happiness = pm.Normal('happiness',
mu_happ,
sd_happ,
observed=data['happiness'])
# Create model instance for Lumen
m = ProbabilisticPymc3Model(modelname,
allbus_model,
shared_vars={'age': age})
if fit:
m.fit(data)
return data, m
def create_pymc3_simplest_model(modelname='pymc3_simplest_model', fit=True):
if fit:
modelname = modelname + '_fitted'
np.random.seed(2)
size = 100
mu = np.random.normal(0, 1, size=size)
sigma = 1
X = np.random.normal(mu, sigma, size=size)
data = pd.DataFrame({'X': X})
basic_model = pm.Model()
with basic_model:
sigma = 1
mu = pm.Normal('mu', mu=0, sd=sigma)
X = pm.Normal('X', mu=mu, sd=sigma, observed=data['X'])
m = ProbabilisticPymc3Model(modelname, basic_model)
if fit:
m.fit(data)
return data, m
def create_pymc3_eight_schools_model(modelname='pymc3_eight_schools_model',
fit=True):
if fit:
modelname = modelname + '_fitted'
scores = np.array([28.39, 7.94, -2.75, 6.82, -0.64, 0.63, 18.01, 12.16])
standard_errors = np.array([14.9, 10.2, 16.3, 11.0, 9.4, 11.4, 10.4, 17.6])
data = pd.DataFrame({
'test_scores': scores,
'standard_errors': standard_errors
})
standard_errors = theano.shared(standard_errors)
with pm.Model() as normal_normal_model:
tau = pm.Uniform('tau', lower=0, upper=10)
mu = pm.Uniform('mu', lower=0, upper=10)
theta_1 = pm.Normal('theta_1', mu=mu, sd=tau)
theta_2 = pm.Normal('theta_2', mu=mu, sd=tau)
theta_3 = pm.Normal('theta_3', mu=mu, sd=tau)
theta_4 = pm.Normal('theta_4', mu=mu, sd=tau)
theta_5 = pm.Normal('theta_5', mu=mu, sd=tau)
theta_6 = pm.Normal('theta_6', mu=mu, sd=tau)
theta_7 = pm.Normal('theta_7', mu=mu, sd=tau)
theta_8 = pm.Normal('theta_8', mu=mu, sd=tau)
test_scores = pm.Normal('test_scores',
mu=[
theta_1, theta_2, theta_3, theta_4,
theta_5, theta_6, theta_7, theta_8
],
sd=standard_errors,
observed=data['test_scores'])
m = ProbabilisticPymc3Model(
modelname,
normal_normal_model,
shared_vars={'standard_errors': standard_errors},
fixed_data_length=True)
if fit:
m.fit(data)
return data, m