jan 2014 intro to bayesian probability, statistical inference, sampling
DESCRIPTION
Introduction to Probability, Conditional Probability, Bayes's Rule, Example of Sampling Problem using Bayes's Theorem, story from Howard RaiffaTRANSCRIPT
A = person entering our clinichas lung cancer = 10% = 0.1
B = person entering our clinicis a smoker = 50% = 0.5
Likelihood data = P(B|A) = 0.8
P(A|B) = (0.8) x (0.1)
(0.5)= 0.16
• “Bayesian Inference” refers to use of Bayes’Theorem to update probabilities as newevidence is available
• Especially valuable to analyze trends when data will continue to flow in over time
• Provides a rational method for updatingbeliefs in science, engineering, medicine, law
Sets
Venn Diagrams
Terminology
Symbols
Experiment Space S
A
B
A B
A B
Intersection of sets = creatures satisfying both constraints: two-legged And flying
∩ the “and” function
A B
Caution: Venn Diagrams areLogical relationships,
not the comparative size of sets.
A B
A B
A B
Union: e.g. creatures satisfying either constraint: two-legged or flying
the “or” function
What if no intersection?
A ∩ B = (null set, empty set, or impossible event)
A B
S is the set of all possible outcomes S is often called “the sure event”
EVENT = subset of S A S
if A is an event, Anot is the eventthat A does not occur
A Anot = null, impossible set
A Anot = S set of all outcomes
the probability of A, given B
P(A│B)
Ask some lawyers whotry cases on probabilistic
evidence?
Ask political punditswho make election
predictions?
Ask a class of MBA studentsat Harvard B-School
taking a course inDecision Theory?
