abhijeet-talaulikar

posterior = pm.sample_posterior_predictive(trace, mmm)
predictions = posterior['posterior_predictive']['revenue'].mean(axis=0).mean(axis=0) * media['REVENUE'].mean()

media_decomp = pd.DataFrame({i:np.array(trace['posterior']["contribution_"+str(i)]).mean(axis=(0,1)) for i in channel_priors.keys()}, index=dates) * media['REVENUE'].mean()

plt.plot(media['REVENUE'])
plt.plot(predictions)
plt.title("Model Fit")

abhijeet-talaulikar

current_revenue = media_roi['revenue'].sum()
current_budget = media_roi['spend'].sum()
new_budget = current_budget * 1.05

abhijeet-talaulikar

# initialize model
opt_model = grb.Model(name="Media Budget Optimization")

x_vars = opt_model.addVars(media_roi['media'], vtype=grb.GRB.CONTINUOUS,
              lb=0, name="media")

# keep total spend less than new available budget
opt_model.addConstr(sum(x_vars[i] for i in media_roi['media']) <=
             new_budget, name="New Budget")

abhijeet-talaulikar

# Value of the objective function (ROI) 
print(f"The Optimal Objective Value {opt_model.objVal}")
# Values of decision variables (Funds allocated to each channel)
opt_df = pd.DataFrame.from_dict(x_vars, orient="index", columns=["Variable Object"])
opt_df.reset_index(inplace=True)
opt_df.rename(columns={"index": "Media"}, inplace=True)
opt_df["Budget Allocated"] = opt_df["Variable Object"].apply(lambda item: item.X)

plt.bar(opt_df["Media"], opt_df["Budget Allocated"])
plt.xlabel("Media")

abhijeet-talaulikar

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)

abhijeet-talaulikar

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)

abhijeet-talaulikar

rolling_channel_coefficient = pm.GaussianRandomWalk(
    f"coefficient_{channel}",
    sigma=sigma_walk,
    init_dist=pm.Normal.dist(channel_prior, 0.01),
    dims="time"
)

abhijeet-talaulikar

mmm, trace = BayesianMMM("W")

import matplotlib.pyplot as plt

plt.figure(figsize=(15,5))

for channel in ['CTV', 'DIRECT_MAIL', 'EMAIL', 'TV']:
  plt.plot(
      trace.posterior[f'coefficient_{channel}'].values.mean(axis=(0,1)), 
      linewidth=2, 

abhijeet-talaulikar

mmm, trace = BayesianMMM("Q")

paid_search_df = pd.DataFrame({
    'quarter': "Quarter "+pd.PeriodIndex(dates, freq='Q').astype(str).str[-1].astype(str).values,
    'coefficient': trace['posterior']['coefficient_PAID_SEARCH'].mean(axis=(0,1))
})

paid_search_df.groupby('quarter').mean().plot.bar();
plt.title("Paid Search Effectiveness over Quarters")
plt.ylim(bottom=0.12)

abhijeet-talaulikar

mmm, trace = BayesianMMM("YoY")

paid_search_df = pd.DataFrame({
    'year': np.array(["Year before that"]*52 + ["Last Year"]*52),
    'coefficient': trace['posterior']['coefficient_PAID_SEARCH'].mean(axis=(0,1))
})

display(paid_search_df.groupby('year').mean())

paid_search_df.groupby('year').mean().plot.bar();