Bayesian inference in marketing

Bayesian inference allows for decision making and market research evaluation under uncertainty and limited data.

Bayesian statisticians can use both an objective and a subjective approach when interpreting the prior probability, which is then updated in light of new relevant information.

The concept is a manipulation of conditional probabilities:[3] Alternatively, a more simple understanding of the formula may be reached by substituting the events

[11] Assessments are made by a decision maker on the probabilities of events that determine the profitability of alternative actions where the outcomes are uncertain.

The decision maker can decide how much research, if any, needs to be conducted in order to investigate the consequences associated with the courses of action under evaluation.

The theorem provides a formal reconciliation between judgment expressed quantitatively in the prior distribution and the statistical evidence of the experiment.

By reviewing the posterior (which then becomes the new prior) on regular intervals throughout the development stage managers are able to make the best possible decision with the information available at hand.

Although the review process may delay further development and increase costs, it can help greatly to reduce uncertainty in high risk decisions.

This method of evaluating possible pricing strategies does have its limitations as it requires a number of assumptions to be made about the market place in which an organisation operates.

As markets are dynamic environments it is often difficult to fully apply Bayesian decision theory to pricing strategies without simplifying the model.

In order to help provide further information the method can be used that produces results in a profit or loss aspect.

Bayesian decision making under uncertainty lets a marketing manager assess his/her options for channel logistics by computing the most profitable method choice.

Identifying and quantifying all of the relevant information for this process can be very time-consuming and costly if the analysis delays possible future earnings.

Bayes is also useful when explaining the findings in a probability sense to people who are less familiar and comfortable with comprehending statistics.

It is in this sense that Bayesian methods are thought of as having created a bridge between business judgments and statistics for the purpose of decision-making.

It allows for the incorporation of prior information when available to increase the robustness of the solutions, as well as taking into consideration the costs and risks that are associated with choosing alternative decisions.

It is considered the most appropriate way to update beliefs by welcoming the incorporation of new information, as is seen through the probability distributions (see Savage[15] and De Finetti[16]).

Bayes methods are more cost-effective than the traditional frequentist take on marketing research and subsequent decision making.

The planning and implementation of trials to see how a decision impacts in the 'field' e.g. observing consumers reaction to a relabeling of a product, is time-consuming and costly, a method many firms cannot afford.

In place of taking the frequentist route in aiming for a universally acceptable conclusion through iteration,[18] it is sometimes more effective to take advantage of all the information available to the firm to work out the 'best' decision at the time, and then subsequently when new knowledge is obtained, revise the posterior distribution to be then used as the prior, thus the inferences continue to logically contribute to one another based on Bayes theorem.

Instead the model has been proven as useful as a qualitative means of describing how individuals combine new evidence with their predetermined judgements.

The advertising manager can characterize the outcomes based on past experience and knowledge and devise some possible events that are more likely to occur than others.

Based on the outcome of the experiment he can re-evaluate his prior probability and make a decision on whether to go ahead with increasing the advertising in the market or not.

If so, how much needs to be collected and by what means and finally, how does the decision maker revise his prior judgment in light of the results of the new experimental evidence?

In this example the advertising manager can use the Bayesian approach to deal with his dilemma and update his prior judgments in light of new information he gains.

He needs to take into account the profit (utility) attached to the alternative acts under different events and the value versus cost of information in order to make his optimal decision on how to proceed.

Markov chain Monte Carlo (MCMC) is a flexible procedure designed to fit a variety of Bayesian models.

The advancements and developments of these types of statistical software have allowed for the growth of Bayes by offering ease of calculation.

This is achieved by the generation of samples from the posterior distributions, which are then used to produce a range of options or strategies which are allocated numerical weights.

The decision maker can then assess the results from the output data set and choose the best option to proceed.