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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 has always proven difficult since there are none or limited data upon which such decisions can be based on (Hitendra, 2017).

This calls for the Bayesian probabilistic approach to help in the decision making by determination of chances of an event happening in the future.

The use of Bayesian theorem under the above given circumstances would employ inferences through mathematical principles and concepts of probability, enabling us to assess the numerical probabilities in a bid to provide solutions to real-life marketing problems. In his work, Christoph (2018) postulates that opinions are expressed in probabilities, data collected, and these data change the prior probabilities to yield posterior probabilities.

Bayesian theorem relies on a prior probability of an event occurring, and takes advantage of manipulating the conditional probability, which in its simplest form is expressed as;

P(AB)=P(AB) P(B)=P(BA) P(A) … (i)

To simplify the above equation using our previous problem in marketing, the given events A and B in the above equation can be substituted by hypothesis (H) and data (D).

The likely function can then be given by the expression P(DH), and evaluates the likelihood of the observed data coming from the given set of hypotheses. The initial probability to be manipulated if given by P(H) while the recalculate probability if P(D) found by integrating P(DH), P(H) and P(HD).

## Most Appropriate Approach to Solve The Problem

Substituting the above variables into equation (i) and rearranging yields the equation below.

P(HD) = P(DH) P(H) …(ii)

P(D)

As discussed by Abbas (2019), when making marketing decisions about uncertain outcomes, the probability of events that may lead to profitability of alternative actions can be determined by the Bayesian theorem, resulting into more informed decisions. This is done by combining a set of actions and events then computing the corresponding expected profits for all the sets 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.

A methodology that involves the use of decision trees is used in analysis. In cases of favourable payoff being predicted, the project is given greenlights to proceed, otherwise it is stopped. High risk decisions are therefore avoided by having managers constantly reviewing the posterior (which is now essentially the new prior) and making informed choices by the available information (Mark, 2014).

A market research reveals the wholesale and retail prices, market size and its composition, all which are useful in providing initial information. A range of pricing strategies is then evaluated with the help of managerial judgement after making certain assumptions on the nature of the business environment, hence this is one area that the Bayesian approach comes handy to offer solutions for a real-life problem in business organisation (Alexander, 2017).

When promoting a new product or service, the marketing manager needs to consult the experienced senior executives to incorporate their judgements after modifying them a bit in respect to the market and economic complexities. In one of the studies, Oswald (2013) explained that it is proper to employ Bayesian approach by using test samples that will determine the effectiveness of the promotion before launching a full-fledged campaign. The data obtained from the previous test samples provides prior information useful in determining the possible occurrence of events.

Every business organisation has their own channels of doing things and the channels of distribution. Apparently, nearly all processes can be viewed from the perspective of profitability or losses, (Alexander, 2017). This necessitates the need to obtain prior information in selecting the channel selection process. Such initial information may be costs, expenses incurred in trainings and expected profits. Using Bayesian approach, the manager is able to assess the options of the channel logistics after calculating the highest profitable channel.

Even though most business organisations find it desirable to use Bayesian probabilistic approach to solve the problems associated with the marketing, it suffers a number of setbacks as there are weaknesses when it comes to every mathematical model of solving problems (Hitendra, 2015).

In his work, Andrew (2013) found that marketing studies require prior information which is accurately chosen and well understood. Unlikely for the Bayesian analysis, there is not correct way of choosing prior information thus care has to be taken when making inference and drawing mathematical models by examining assumptions made carefully.

Mark (2014) postulated that the process of identifying and quantifying all the relevant information takes a lot of time and are associated with high costs if the future earnings are delayed by the analysis process.

Markets are a dynamic environment hence it is challenging to use the Bayesian analysis in pricing strategies unless the models are simplified.

References

Abbas, K. (2019). Bayesian Analysis of Three-Parameter Frenchet Distribution with Medical Applications. Computational and Mathematical Methods in medicine, 2019(1), 1-8.

Alexander, E. (2017). Introduction to Bayesian Inference for Psychology. ResearchGates.

Andrew, G. (2013). Philosophy and the practice of Bayesian statistics. New York.

Christoph, K. (2018). Bayesian statistics in education research: A look at the current state of affairs. Educational Review, 70(4), 30-75.

Eadie, G. (2019). Introducing Bayesian Analysis with m&m's: An active learning exercise for undergraduates. Journal of Statistics Education, 27(2), 60-67.

Hitendra, D. P. (2017, March 14-15). Application of Bayesian Decision Theory in Management Research Problems. International Journal of Scientific Research Engineering & Technology, pp. 191-194.

Karni, E. (2012, May 30). A theory of Bayesian decision making with action-dependent subjective probabilities. Research Article, pp. 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. Management.