Unlocking Insights with Bayesian Modeling

In the dynamic realm of marketing, understanding and optimizing the allocation of your marketing budget is crucial. PyMC-Marketing, a powerful Bayesian modeling framework, offers a sophisticated approach to crafting a Marketing Mix Model (MMM) that not only adapts to the ever-changing marketing landscape but also provides deeper insights into the efficacy of different marketing channels.

Why Choose PyMC-Marketing?

PyMC-Marketing stands out due to its Bayesian framework, offering flexibility and depth in understanding marketing dynamics. Unlike traditional models, it allows for incorporating prior knowledge and beliefs into the analysis, leading to more nuanced and robust predictions. This approach is particularly beneficial in a marketing context where past data and expert knowledge are vital in shaping future strategies.

Steps to Build Your MMM with PyMC-Marketing

1. Preparing Your Data

Begin with collecting and organizing your marketing data. This should include:

• Sales data (your target variable).
• Media spend across various channels (e.g., TV, online).
• Control variables that might affect sales (like holidays or economic trends).

2. Setting Up Your Environment

Ensure you have PyMC-Marketing installed. If not, set it up using:

conda create -c conda-forge -n marketing_env pymc-marketing
conda activate marketing_env

3. Model Specification with DelayedSaturatedMMM

PyMC-Marketing provides the DelayedSaturatedMMM class, which simplifies the process by handling scaling of data and providing diagnostics and reporting plots. Here’s how to specify your model:

• Define your channel contributions using appropriate distributions, such as a HalfNormal distribution for positive contributions. Use your domain knowledge to set the sigma parameter, which controls the variance.

from pymc_marketing.mmm import DelayedSaturatedMMM

# Define your model
mmm = DelayedSaturatedMMM(
    date_column="your_date_column",
    channel_columns=["channel1", "channel2"],
    control_columns=["control1", "control2"],
    adstock_max_lag=8,
    yearly_seasonality=2,
)

• Customize your priors if needed, to reflect your specific assumptions or past knowledge.

Compute Spend Share (Optional)

If you are using spend share as part of your prior, compute it from your data. For example:

total_spend_per_channel = data[["channel1", "channel2"]].sum(axis=0)
spend_share = total_spend_per_channel / total_spend_per_channel.sum()

Specify Custom Priors

Now, specify your custom priors. This involves creating a dictionary that matches the structure required by the DelayedSaturatedMMM class.

Start with Default Model Configuration: Get the default model configuration and use it as a base

default_model_config = mmm.default_model_config

Define Your Custom Priors: Create a dictionary with your custom priors. Here’s an example where we customize the beta_channel prior using a LogNormal distribution and adjust its mu and sigma parameters based on your spend share or other criteria.

import numpy as np

# Example of customizing the beta_channel prior
custom_beta_channel_prior = {
    'beta_channel': {
        'dist': 'LogNormal',
        "kwargs": {
            "mu": np.array([2, 1]),  # Example values, adjust based on your data
            "sigma": np.array([2.1775326, 1.14026088])  # Example values, adjust based on your data or spend share
        }
    }
}

Merge Custom Priors with Default Configuration: Combine your custom priors with the default configuration.

my_model_config = {**default_model_config, **custom_beta_channel_prior}

Apply Custom Configuration to Model

Finally, apply your custom configuration to the model.

mmm = DelayedSaturatedMMM(
    model_config=my_model_config,
    # other configurations as before...
)

4. Fitting the Model

Now, fit the model using your data.

X = data.drop('sales', axis=1) y = data['sales'] mmm.fit(X, y)

5. Analyzing the Results

Post-fitting, delve into the results:

• Use mmm.plot_components_contributions() to visualize contributions from different channels.

• Check the model diagnostics and ensure your model’s robustness.

6. Posterior Predictive Checks

Perform posterior predictive checks to ensure your model’s predictions align well with the actual data.

with mmm.model:
posterior_predictive = pm.sample_posterior_predictive(mmm.trace)

For a visual comparison, you can plot the actual sales data against the predicted sales.

mmm.plot_posterior_predictive(original_scale=True);

Statistical Comparison

You can also calculate summary statistics like RMSE (Root Mean Squared Error) to quantitatively assess the model’s performance:

from sklearn.metrics import mean_squared_error
rmse = np.sqrt(mean_squared_error(y, predicted_sales))
print(f"Root Mean Squared Error: {rmse}")

7. Integrating Insights into Your Strategy

Leverage the insights gained from your MMM to optimize your marketing budget allocation, ensuring that your spend is directed towards the most effective channels.

The Power of Understanding Long-term Effects

One of the unique advantages of PyMC-Marketing is its ability to model the long-term impact of advertising. This is crucial for developing effective marketing strategies that go beyond short-term gains.

Wrapping Up

PyMC-Marketing offers a cutting-edge approach to MMM, providing deeper insights and more flexible modeling capabilities. By integrating this tool into your marketing analytics arsenal, you can make more informed decisions, optimize your marketing spend, and ultimately drive better business outcomes.