# Understanding Prior and Posterior Distributions in Media Mix Models

This document summarizes the outputs of a statistical model known as a media mix model, which helps understand how different marketing channels affect outcomes like sales or conversions.

## What are Prior and Posterior Distributions?

In the context of this analysis:

- Prior Distribution: This represents our initial beliefs about how the effects of different marketing channels might look based on past information before seeing the new data.
- Posterior Distribution: After analyzing new data, this reflects our updated beliefs about these effects, integrating both prior knowledge and the new evidence.

## Visual Representation

The generated output consists of plots that compare these two distributions across different parameters of the media mix model. Each plot typically has:

- X-Axis: Represents the parameter values for a given marketing channel.
- Y-Axis: Shows the likelihood of each value based on either prior or posterior data.
- Lines: Different colors indicate prior (blue) and posterior (orange) distributions, allowing for easy comparison.

## Why is This Important?

Understanding these distributions helps marketers make informed decisions by illustrating how different channels interact and contribute to overall performance. The differences between the prior and posterior distributions highlight the influence of new data and aid in optimizing marketing strategies.