All you need to know about Bayesian marketing mix modeling – Analytics India Magazine

Algorithms from machine learning can have their usage in a variety of fields. We can see as these algorithms are emerging in a particular field, some other algorithms or some updates on the old algorithms are also introduced in a similar field. Marketing Mix Models (MMMs) are very helpful tools in the field of marketing and media. Bayesian marketing mix models are the update of MMMs and both of them basically use a kind of machine learning algorithms. In the series of articles, we will discuss both of these models in detail. The major points to be discussed in part one of the article are listed below.
Table of Contents
Let’s start by introducing the marketing mix modelling.
What is Marketing Mix Modelling?
Marketing mix modelling is a kind of statistical analysis that helps in improving the capacity and performance of sales and marketing. Multivariate regressions analysis can be an example of this kind of analysis. The main motive behind this kind of analysis and modelling is to know about the impact on benefits of a company when they are using or implying any special and specific tactic. Also forecasting the impact of future sets of tactics comes under the marketing mix modelling.
In the recent scenario, MMM can be considered as a trustworthy marketing tool for companies that are based on consumer marketing. Since a manufacturing and marketing company can have access to all the data of sales and marketing support, using such data we can perform analysis which can be the reason for the explosion in future sales and benefits of a company or any organization. Talking about the usage of marketing mix modelling, using the rich insights of MMM, we can perform the following tasks:
The above-given image is a representation of the basic flow structure marketing mix modelling. In the next section, we will discuss the working of the marketing mix modelling.
Working of Marketing Mix Models
As discussed above, we can consider these models as a technique of simple regression modelling techniques.  The motive of MMM can be defined as the estimation of the impact of marketing strategies or any other drivers on the component of interest. Examples of components can be the change in sales or the change in the number of customers per week.
Let’s say the estimation can be done using the following predictor variables:
The relative importance of the predictors can be estimated by the linear regression of the set of coefficients. This statement can also be considered as the basic approach of the MMMs. Talking about the real-world problems, MMMs are required to deal with the non-linear factors also so that they can capture the effect of marketing strategies on the behaviour of consumers or in the changes of the sales accurately. Some of the functions MMMs  requires to optimize the marketing strategies are as follows:  
Marketing spend
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In this section, we have seen a basic working introduction of the traditional marketing mix models but there are some problems with these models which we will; be discussing in the next section.
Problems with Traditional Marketing Mix Models
In the above section, we have seen that we use the MMMs to know the individual effect of different variables like marketing expenditure and customer behaviour, or pricing. Also, we got to know that the traditional models are using regression analysis in depth. The sparsity of the data is one of the most basic problems which is very complex to analyze using simple models like linear regression. We can say that using these models is trying to estimate things in a space where we have thousands of observations with many outliers.
The above sparsity can generate the problem of overfitting the simple models. When going more into algorithms of these kinds of models these are generated to fit the noise or variations in the data instead of fitting the trend of the data. This fitting problem can lead to wrong forecasting of the marketing strategies.    
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The above image is an example of the overfitting problem where the red line can be considered as a model which is perfectly fitted with every data point and also an example of over-fitting. 
Another reason for the failure of the traditional MMMs is that they are not much eligible to equip the hard data with prior knowledge. The simple models are defined with the parameters which are independent of each other. In such scenarios modelling of the marketing data where every component of the data is very relatable and dependent on each other is complex and mostly fails to cover every point. 
To deal with such problems we are required to incorporate such domain knowledge using which we can guide the model in the right direction. Here Bayesian methods can be helpful. In the next section, we will be looking at how Bayesian MMMs help in improving the traditional MMMs.
Bayesian Market Mix Modelling to Rescue
In the above section, we have discussed that the traditional MMMs use simpler models that are not able to handle the complexity of the marketing data. Talking about Bayesian statistics, these are a branch of probability theory, and usage in the MMMs field was first introduced by Google in 2017 [Jin et al 2017]. One of the most common and important things about probability theory and Bayesian statistics is that they can include domain knowledge. 
Inclusion of the domain knowledge can be expressed through what is known as priors. Using prior we are capable of including the prior knowledge, domain knowledge, and information about the parameters of the model. More formally we can say that the prior is a probability distribution that can encode the marketing intuition and certainty about the parameters in the MMMs field. Combining the likelihood and prior we produce the posterior.  Here in the MMMs, we can consider the information about the data as the likelihood. 
This combination of prior and likelihood or we can say posterior represents the information of the model. Using it for measuring marketing effectiveness we call it Total Marketing Modeling. Using the bayesian statistics we guide the model to how we know that marketing works from experience and prior knowledge.
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The above image is a representation of the Bayesian modelling of a single variable. Where the intuition behind the modelling can be expressed as the prior and the information about the data is the likelihood and the combination of prior and likelihood is posterior. 
Final Words
In this article, we have discussed the market mix modelling in which we have seen what are the functions which are required to estimate the predictors and what are the problems with the traditional MMMs. Along with that we have seen a solution for the problems that basically follow the Bayesian statistics. 
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