# Bayesian Probabilistic Approach For Forecasting Sales Impact

## Bayesian Probabilistic Approach For Forecasting Sales Impact

### Problem Statement

Identify The Need To Better Forecast The Impact Of An Event On Sales Where You Need To Identify If You Will Adopt a Bayesian Probabilistic Approach

In order to improve customer relationship, most business organisations put in place favourable policies enabling them to boost sales and increase profits. One of the departments given considerable attention is the marketing department, as it forms one of the most important branches of management sciences.

Marketing is essential in communicating the value of products and services to customers, thus an elaborate market research will enable the business organisation to choose the target markets more appropriately amidst future uncertainties and limited data to act upon (Christoph, 2018). Effective marketing management therefore seeks to understand customer behaviour and their unpredictability over a range of business parameters in order to balance their requirement and the economics, and ultimately building a healthy relationship between the customers and the business organisation.

More often than not, decisions made in marketing strategies especially when a new product or service is rolled out into market requires an extensive market research to identify target markets and consumer potentials, as well as other economic patterns. This always proves difficult as the data on which such decisions are based is non-existent or limited (Hitendra, 2017).

This requires a Bayesian probabilistic approach that helps in decision making by determining the probability of an event occurring in the future.

Using Bayes’ Theorem in the above situations allows us to leverage reasoning using mathematical principles and probability concepts to evaluate numerical probabilities and provide solutions to real-world marketing problems. In his work, Christoph (2018) assumes that opinions are expressed in probabilities, that data are collected, and that these data modify prior probabilities and produce posterior probabilities.

Bayes’ theorem relies on an a priori probability that an event will occur and uses operations on conditional probabilities. In its simplest form, this is expressed as:

P(AB)=P(A\B) P(B)=P(B\A) P(A) … (i)

To simplify the above equation based on the previous marketing problem, we can replace certain events A and B in the above equation with hypothesis (H) and data (D). The likelihood function is given by the formula P(D\H) and evaluates the likelihood that the observed data originates from a given set of hypotheses. The initial operation probability given by P(H) and the recalculation probability given by P(D) are obtained by integrating P(D\H), P(H), and P(H\D). is required by.

The most appropriate approach to solve the problem
Substituting the above variables into equation (i) and rearranging, we get the following equation:

P(H\D) = P(D\H) P(H) …(ii)

P(D)

As Abbas (2019) explains, when making marketing decisions about uncertain outcomes, the probability of an event that could lead to the profitability of an alternative action can be determined by Bayes’ theorem, and more leads to more informed decision-making. This is done by combining a set of actions and events and calculating the expected profit corresponding to every group of actions and events. The resulting profit margins are then assessed before the final decision is made.

In this paper, there are four areas in marketing that are explored extensively and how the use of Bayesian approach could be the most efficient in providing solutions. These are discussed below.

The marketing manager employs the use of the already existing prior information, however limited it may be. Oswald (2013) discussed that during a product development phase, a comparison is made of the additional review project cost with the value of added information so as to lower the cost of uncertainty. The analysis uses a methodology that includes the use of decision trees. If positive profitability is foreseeable, the project is given the green light to continue, otherwise it is abandoned. Therefore, risky decisions are avoided if managers constantly review their post-processes (now essentially new ex-ante processes) and make informed decisions based on available information ( Mark, 2014).

Market research reveals wholesale and retail prices, market size and its composition, which can serve as initial information. A range of pricing strategies is then evaluated based on business judgment, making certain assumptions about the nature of the business environment. Therefore, this is an area where Bayesian approaches are useful in providing solutions to real-world problems in business organizations (Alexander, 2017). When promoting a new product or service, marketing managers should consult experienced managers and consider their judgments after making slight modifications to account for market and economic complexities. In one of his studies, Oswald (2013) explains that it is appropriate to apply a Bayesian approach and use test samples to determine the effectiveness of advertising before launching a comprehensive campaign. Did. Data obtained from previous test samples provides preliminary information to help determine the likelihood of an event occurring.

Every business organization has its own activity and sales channels. Apparently, almost any process can be viewed in terms of profitability or loss (Alexander, 2017). Therefore, when selecting a channel selection method, it is necessary to obtain information in advance. Such initial information may include costs, training fees, and anticipated benefits. Using a Bayesian approach, managers can evaluate channel logistics options after calculating the most profitable channel.

Although most business organizations consider it desirable to use a Bayesian probabilistic approach to solve problems related to marketing, all mathematical models for solving problems have weaknesses. It has suffered many setbacks (Hitendra, 2015).

Andrew (2013) states in his book that marketing research requires carefully selected and well-understood prior information. For Bayesian analysis, it is unlikely that there is a correct way to select prior information. Therefore, care must be taken when carefully considering assumptions and drawing conclusions and drawing mathematical models.

Mark (2014) argues that the process of identifying and quantifying all relevant information takes a long time and incurs high costs if the analysis process delays future revenue.

Because the market is a dynamic environment, it is difficult to use Bayesian analysis for pricing strategy if the model is not simplified.

#### References

Abbas, K. (2019). Bayesian analysis of three-parameter Franche distributions for medical applications. Computer Aided and Mathematical Methods in Medicine, 2019(1), 1-8.

Alexander, E. (2017). An introduction to Bayesian inference for psychology. Research Gates.

Andreas, G. (year 2013). Philosophy and practice of Bayesian statistics. new york.

Christoph, K. (2018). Bayesian statistics in educational research: An overview of the current state of affairs. Education Review, 70(4), 30-75.

Eadie, G. (2019). An introduction to Bayesian analysis with M&M’s: An active learning exercise for students. Journal of Statistics Education, 27(2), 60-67.

Hitendra, D. P. (2017, March 14-15). Application of Bayesian decision theory to management research problems. International Journal of Scientific Research, Engineering and Technology, S. 191-194。

Carni, E. (May 30, 2012). A theory of Bayesian decision making using subjective probabilities that depend on behavior. Research paper, pages 125-146.

Mark, W. (2014). Bayesian statistics. Journal of Applied Statistics, 40(12), 2773-2774.

Oswald, F. (2013). Bayesian probability and statistics in management research.

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