Created
June 30, 2023 22:44
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def BayesianMMM(splits="W"): | |
if splits == "Q": | |
time_series = pd.PeriodIndex(dates, freq='Q').astype(str).str[-1].astype(int).values | |
elif splits == "H": | |
time_series = pd.PeriodIndex(dates, freq='Q').astype(str).str[-1].map({'1':1, '2':1, '3':2, '4':2}).values | |
elif splits == "YoY": | |
time_series = np.array([1]*52 + [2]*52) | |
else: | |
time_series = np.arange(104) | |
def scale(x, y): | |
return x * y.sum() / x.sum() | |
with pm.Model(coords={"time": time_series}) as mmm: | |
target = media_transformed['REVENUE'] / media_transformed['REVENUE'].mean() | |
# std of random walk | |
sigma_walk = pm.Uniform("sigma_walk", lower=0, upper=1) | |
media_contributions = [] | |
for channel in channel_priors.keys(): | |
# define coefficient | |
channel_prior = channel_priors[channel] | |
rolling_channel_coefficient = pm.GaussianRandomWalk( | |
f"coefficient_{channel}", | |
sigma=sigma_walk, | |
init_dist=pm.Normal.dist(channel_prior, 0.01), | |
dims="time" | |
) | |
# define saturation | |
alpha = pm.Uniform(f"alpha_{channel}", lower=0.5, upper=2) | |
gamma = pm.Uniform(f"gamma_{channel}", lower=0.5, upper=1.5) | |
saturated_media = hill_transform( | |
pt.as_tensor_variable(media_transformed[channel] / media_transformed[channel].mean()), | |
alpha, | |
gamma | |
) | |
scaled_media = scale(saturated_media, target) | |
scaled_media /= scaled_media.mean() | |
# contribution | |
channel_contribution = pm.Deterministic(f"contribution_{channel}", rolling_channel_coefficient * scaled_media) | |
media_contributions.append(channel_contribution) | |
# controls | |
holiday_coefficient = pm.TruncatedNormal("coefficient_holiday", mu=holiday_prior, sigma=0.0001, lower=0) | |
controls = pm.Deterministic("contribution_holiday", holiday_coefficient * scale(pt.as_tensor_variable(bias['holiday_period']), target)) | |
# trend | |
trend_coefficient = pm.Normal("coefficient_trend", mu=trend_prior, sigma=0.0001) | |
trend = pm.Deterministic("contribution_trend", trend_coefficient * pt.as_tensor_variable(target.shift(1).fillna(method='backfill'))) | |
# seasonality | |
seasonality = [] | |
for i in np.arange(1,d+1): | |
coeff_cos = pm.Normal(f"coefficient_seasonality_cos_{i}", mu=seasonality_prior, sigma=0.0001) | |
coeff_sin = pm.Normal(f"coefficient_seasonality_sin_{i}", mu=seasonality_prior, sigma=0.0001) | |
cos_term = pm.Deterministic(f"contribution_seasonality_cos_{i}", coeff_cos * pt.as_tensor_variable(bias[f"cos_{i}"]) * target.sum()/26) | |
sin_term = pm.Deterministic(f"contribution_seasonality_sin_{i}", coeff_sin * pt.as_tensor_variable(bias[f"sin_{i}"]) * target.sum()/26) | |
seasonality.extend([cos_term, sin_term]) | |
noise = pm.Uniform("sigma", lower=0, upper=0.02) | |
intercept_coefficient = pm.TruncatedNormal("coefficient_intercept", mu=0.5, sigma=0.0001, lower=0) | |
intercept = pm.Deterministic("contribution_intercept", intercept_coefficient * target.mean()) | |
# define likelihood | |
likelihood = pm.Normal("revenue", | |
mu = intercept + trend + sum(seasonality) + sum(media_contributions), | |
sigma = noise, | |
observed=target) | |
# inference | |
trace = pm.sample(tune=1000, chains=1) | |
return mmm, trace |
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