Analyzing Marketing Problems: Formulating a Bayesian Solution

This report focuses on formulating a Bayesian solution to address common marketing challenges. It begins by highlighting the importance of marketing in business and the need for effective decision-making, particularly when dealing with limited data. The report then introduces the Bayesian probabilistic approach as a valuable tool for making informed decisions by assessing probabilities. It explores how the Bayesian theorem can be applied to real-life marketing scenarios, such as new product launches, pricing strategies, promotional campaigns, and channel logistics. The report provides a detailed analysis of each area, demonstrating how Bayesian methods can improve decision-making. Furthermore, the report acknowledges the limitations of the Bayesian approach, emphasizing the need for accurate prior information and the challenges of simplifying dynamic market environments. Overall, the report provides valuable insights into the application of Bayesian analysis in marketing and its potential to improve business outcomes.

Running head: FORMULATING A BAYESIAN SOLUTION 1
Quantitative Business Analysis
Objectives
The main objective of this paper is to review scholarly articles in order to identify a common
problem at workplace and formulate a Bayesian solution to it.
Introduction
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.
Problem statement
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).

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This calls for the Bayesian probabilistic approach to help in the decision making by
determination of chances of an event happening in the future.
Most appropriate approach to solve the problem
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(A\B) P(B)=P(B\A) 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(D\H), 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(D\
H), P(H) and P(H\D).
Substituting the above variables into equation (i) and rearranging yields the equation below.
P(H\D) = P(D\H) P(H) …(ii)
P(D)

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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.
a) Developing and launching of a new product
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).

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b) Decisions on pricing
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).
c) Campaigns aimed at promoting goods and services
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.
d) Logistics
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.

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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).
Potential limitations of the proposal analysis
 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.

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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.