## Thursday, April 19, 2012

### Bayes Theorem: Summary of Findings (Green Team) 3.5 out of 5

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the 12 articles read in advance (see previous posts) and the discussion among the students and instructor during the Advanced Analytic Techniques class at Mercyhurst University in April 2012 regarding Bayesian Theorem Analysis specifically. This technique was evaluated based on its overall validity, simplicity, flexibility, its ability to effectively use unstructured data and its ease of communication to a decision maker.

Description:
Bayes’ Theorem is a mathematical formula used to objectively analyze new pieces of data and update probabilities of events to produce a forecast. Rather than computing a frequentist statistic, which gives the probability of an event not being by chance, the formula updates the actual probability of an event based on the presence of evidence either supporting or refuting the event. Scientific testing proves the validity of the theorem, and it is applicable to a variety of events, but its simplicity is debatable and it is more confusing to apply to unstructured data. Confidence in the output must be anchored to the analyst’s evaluation of the data.

Strengths:

• Very useful when dealing with statistical data
• Can be applied to qualitative data
• Output is more estimative than frequentist statistics output, thus more easily understood
• Instinctive Bayesian Approach can be used to influence analyst recommendations by understanding where they fall between gullible and stubborn and vacillating, indecisive and overly cautious.
• Can be applied to various fields including law enforcement, business and healthcare
• When used, Bayes takes into account analysts’ biases

Weaknesses:
• It is difficult to learn and explain it to others
• It requires a good understanding of statistics and probability
• It can be time consuming
• It can be confusing and counter-intuitive
• It requires a computer application or software to implement on complex problems for it to be accurate
• Can be hard to communicate it to the decision makers

How-to:

Personal Application of Technique:
Understanding the use of Bayes was demonstrated through two example problems. The first problem showed graphically the impact of testing for disease outbreak. If 10% of the population is diagnosed with a disease and 90% is unaffected, and a test exists with a 90% accuracy rate, what percent of the population that tests positive actually is infected? Natural frequencies eases the understanding of this problem.
• In a population of 1000 people, 100 are infected.
• Of the 100 infected people, 90 receive a true positive result.
• Of the 900 uninfected people, 90 receive a false positive result.
• Given a positive result on the test, chances are even that a person is actually infected (up from 10%)

Rating: 3.5 out of 5

For further information:
http://mathworld.wolfram.com/BayesianAnalysis.html
http://bayesian.org/
http://www.newscientist.com/blogs/bigwideworld/2012/04/does-trusting-your-gut-make-you-unscientific.html