Summary of Findings: Bayesian Statistics ( 4 out of 5 Stars)

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the 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 November 2017 regarding Bayesian Statistics as an Analytic Method specifically. This technique was evaluated based on its overall validity, simplicity, flexibility and its ability to effectively use unstructured data.

Description:

Bayesian Statistics is a method that uses conditional probability and prior knowledge to produce an estimate. It allows for new evidence relatively easily, but can be susceptible to deceptive information. Bayesian statistics allows for individuals to combat two cognitive biases in vividness and recency biases.   

Strengths:

• It provides a natural and principled way of combining prior information with data, within a solid decision theoretical framework
• Calculates conditional probabilities
• Could be cost-effective for a company
• Eliminates overfitting in models
• Method gives a quantitative result to analysis
• Addresses subjectivity in analysis
• Method can provide a numerical value for words of estimative probability

Weaknesses:

• Finding the prior weight is often complicated
• The nuisance parameters must be arranged in the sequence of importance, even though none of them is of intrinsic interest
• It is computationally intensive which can be challenging
• Might be susceptible to deceptive information
• If the parameter of interest changes the whole prior structure may change
• If the sampling rule or design changes the prior will in general change
• It is emphasized that the prior weights are not to be thought of as prior probabilities, raising a question-mark over the interpretation of the posterior
• Many of the formal simplifications arising from all calculations being probabilistic are lost

How-To:

1. Assess probability of prior information: Pr (A)
2. Examine new evidence and probability of evidence: Pr (X|A)
3. Calculate probability of event compared to probability of evidence:

Application of Technique: The class participated in solving the Monty Hall problem, which is an old game show dilema. Monty Hall would offer a choice of three doors two of which contained goats and one contained a car. The contestant would selected one door, after selection Monty would open the door of one of the goat prizes offering the person the choice to stay with their current door or switch to the other door. The class paired up, with one group of 3, and groups were designated to either stay with initial choices, or switch when given new information. The groups were given pieces of paper to simulate the three doors and ran through ten iterations of the simulation to get a baseline given the methodology assigned to each group. The class was then walked through the math of why it was beneficial to switch to the new door, given the new information. This was due to the given prior information that the subject had a ⅔ chance to select a goat during their first selection process.

For Further Information:

1. Bayes Theorem Explained
2. Bayes Theorem Demonstrated with Mammograms
3. The Theory That Would Not Die