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?