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# Baye's Theorem

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## Bess Mersch

on 25 October 2012

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#### Transcript of Baye's Theorem

Bess Mersch Olivia Fox Brian Michael Christopher Shirkey Probability of a certain model of car breaking down
Probability of a pilot being able to complete a task based on experience
Probability of nuclear plant failure at different times or different components (Apostolakis et. All 1980) Doherty and Keeley (1969)
task was to specify the direction of the gap of C
Two conditions
Respond after each stimulus
Respond after 4 consecutive presentation
Using Bayes theorem predicted 4-look performance from 1-look data
Overall hit rates
Pattern of each subjects 4-look data
"The closeness of the predictions to the empirical frequencies is remarkable when one considers that the data are based on a procedure which was neither originally designed to test the Bayesian model, nor is an optimal procedure to do so." Prediction of Behavior/Success Prediction of
Future behavior
Success of systems
Implications on
Judgments
Research
Hypothesis formulation
Interpretation of data Application in Psychology/Engineering Bayesian Statistical Inference for Psychological Research
Edwards, Lindman, and Savage (1963)

pre-existing beliefs and expectations influence judgments of novel health information
Dong-Seon et. Al. (2012)

Insensitivity to prior probability of outcomes: Base rate neglect
Kahneman and Tversky (1973) Influence on Judgments Examples Baye's Theorem What is Bayes’ Theorem?
What does it do?
Why do we need it?
What is the formula? What is Bayes’ Theorem 5% of the population has X disease.
95% of tests correctly identify a positive result when disease is present.
2% of tests detect the disease when it is not present (false positive)
What is the probability that you have disease X if you get a positive result? Formula Explained Probability = outcome / all possibilities
Probability = True positive / (True positive + False negative)
Probability = .0475/(.0475+.019)= .714 Formula Explained P(A|B) – the probability that you have the disease given a positive test
P(B|A) – the probability you have a positive test given you have the disease
P(A) – the probability of a positive test
P(B≠A) – the probability you have a positive test given you do not have the disease
P(≠A) – the probability you do not have the disease

P(A|B) = (.95*.05)/((.95*.05)+(.95*.02)) = .714 In Bayesian: P(A|B)= P(B|A)*P(A)
P(B|A)*P(A)+P(B≠A)*P(≠A) Formula Explained
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