# Bayesian analysis

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Bayesian analysis is a statistical analysis method based on the probability of a mortgage. It follows from Bayes’ law which states conditional probabilities. According to this law, the posterior probability of a parameter p is proportional to the prior probability of parameter p multiplied by the likelihood of p from the collected data.

Bayesian analysis allows us to determine the probability of an event A knowing an event B, if we know the probabilities of A, B and B knowing A. The theorem can thus be formulated as follows: P(A/B) = (P(B/A) P(A) P(B))/(P(B)) In this formula :

• P(A) is the a priori probability of the event A. It is also called “marginal probability of A”. It is prior, i.e. it precedes any information about event B,
• P(B) is the marginal probability of B or a priori of B,
• P(A/B) is the posterior probability of A knowing B or of A under condition B. It is posterior, i.e. it depends directly on B,
• P(B/A) is the likelihood function of A for a known B.

Initially called probability of cause analysis, Bayesian analysis has many applications today. Among the best known applications are those of the doctor who conducts consecutive patient studies to refine the accuracy of his diagnosis. The results of each study and each test he performs must be combined with an a priori knowledge of the patient for his diagnosis to be correct. By doing so, the physician can make a final diagnosis with a known degree of certainty. However, Bayesian analysis can also be applied very well in marketing, especially in the 4 areas of the marketing mix. A decision maker evaluates the probabilities of events that determine the profitability of alternative actions with uncertain outcomes. It also assesses the utility or benefit of each possible combination of events and actions. The decision maker can choose the scope of the research to be conducted to study the consequences of the evaluated action plans. The expected profile can be calculated for each possible action. The decision-maker can therefore turn to the most profitable action. The Baysian analysis results in a formal reconciliation between the statistical evidence of the experiment and the judgment expressed quantitatively in the prior distribution.