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

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

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

# 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

# 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")

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

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

def get_response_curve(channel, start_time, end_time):
    
    def hill_transform(x, alpha, gamma):
        return 1 / (1 + (x/gamma)**-alpha)
    
    # parameters
    coefficient = model.query("variable == @channel")['coefficient'].iloc[0]
    alpha = model.query("variable == @channel")['alpha'].iloc[0]
    gamma = model.query("variable == @channel")['gamma'].iloc[0]
    

abhijeet-talaulikar

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()

media_roi = pd.concat([
    media.drop(['DATE','REVENUE'],axis=1).sum(), 
    media_decomp.sum()
], axis=1).reset_index()

media_roi.columns = ['media','spend','revenue']

media_roi['ROI'] = (media_roi['revenue'] / media_roi['spend'])

abhijeet-talaulikar

bias = pd.DataFrame({
    "t": np.arange(104)
})

d = 2

# Fourier terms
for i in np.arange(1,d+1):
    bias[f"cos_{i}"] = np.cos(2 * np.pi * i * bias["t"] / 52)
    bias[f"sin_{i}"] = np.sin(2 * np.pi * i * bias["t"] / 52)