Bayesian analysis

Bayesian analysis is a useful tool when approaching problems with uncertainty.  This post discusses those situations where Bayesian analysis is appropriate.  It also discusses the assumptions related to Bayesian analysis and problems associated with Bayesian analysis.

Bayesian analysis is useful in situations where there is a degree of uncertainty (Downey, 2013).  The approach is as much a philosophy as it is a technique.  The idea is that there are beliefs which are held before an outcome.  Once an event has been observed the uncertainty related to that event has changed as should the probabilities.  This diachronic interpretation is useful in situations where either knowledge about an event is changing, or the event itself changes over time.

As with any technique, there are strengths and weaknesses to Bayesian analysis.  The strengths include the use of prior information (Anonymous, n.d.).   This approach is intuitive and easy to understand.  This is also a source for a weakness with the approach.  If that prior information is incorrect, it can negatively impact the outcome.  Another weakness of Bayesian approaches is that they view that each may have a different belief related to the probability of an event.  This subjectivity may influence the perception of the approach’s validity.

Bayesian analysis is useful in situations where there is little or no data and requires the use of prior judgment, when there are multiple sources of data and evidence, and lastly when there are many observations and parameters and a high degree of joint probability (Spiegelhalter & Rice, 2009).  One example where there is little or no data is a political election.  Since each election is a unique event, there is little choice but to use evidence and judgment of past situations to attempt to predict the outcome.  An example the application of Bayesian analysis when dealing with a high degree of joint probability is image processing.

References

Anonymous. (n.d.). How can Bayesian methodology be used for reliability evaluation?   Retrieved from http://www.itl.nist.gov/div898/handbook/apr/section1/apr1a.htm#Advantages and Disadvantages of using Bayes

Downey, A. (2013). Think Bayes: O'Reilly Media, Inc.

Spiegelhalter, D., & Rice, K. (2009, 2009/8/7). Bayesian statistics. Scholarpedia.  Retrieved from http://www.scholarpedia.org/article/Bayesian_statistics