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# l1 - Outline Probability Probability Outline Outline 1...

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Outline Probability Sept 13, 2011 Probability

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Outline Outline 1 Introduction to Probability 2 Probability Theory Probability
Introduction to Probability Probability Theory Interpretations Sample Spaces, Events Outline 1 Introduction to Probability 2 Probability Theory Probability

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Introduction to Probability Probability Theory Interpretations Sample Spaces, Events History Probability theory sprang up hand-in-hand with betting . . . eventually Sumarians had dice in roughly 5000 BC Ancient Greeks were fond of betting on astragali (essentially a loaded 4 sided die) The ﬁrst thorough treatment of probability came in the 1560’s by Gerolamo Cardano Established the notion of sample space Pascal, Fermat formalized mathematical approaches to probability in the 1600’s A wealthy gambler commissioned Pascal to study games of chance Probability
Introduction to Probability Probability Theory Interpretations Sample Spaces, Events What is Probability? What’s the probability of a heads on a coin ﬂip? Probability

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Introduction to Probability Probability Theory Interpretations Sample Spaces, Events What is Probability? What’s the probability of a heads on a coin ﬂip? Frequentist: Long run ratio of events to trials The ratio of heads to ﬂips in a very large number of ﬂips Bayesian: Degree of belief Your (hopefully rational and coherent) belief that a ﬂip will come up heads Others: Propensity: Probability is an inherent part of a physical system (think, radioactive decay) Probability
Introduction to Probability Probability Theory Interpretations Sample Spaces, Events A different question What’s the probability that Tim has prostate cancer given a positive PSA test? Frequentist: Lung run ratio of events to trials The ratio of Tims getting cancer to the total number of Tims in a very large number of identical Tims Subjective: Degree of belief Your belief that Tim will get cancer, hopefully informed by useful information like diagnostic tests Probability

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Introduction to Probability Probability Theory Interpretations Sample Spaces, Events Yet another question What’s the probability that a patient with a positive test has cancer? Frequentist? Bayesian? Probability
Introduction to Probability Probability Theory Interpretations Sample Spaces, Events Frequentist and Bayesian interpretations both have their places Frequentist analysis is more “standard” Frequentists dismiss Bayesians as unscientiﬁc Bayesians dismiss frequentists as unscientiﬁc Both have elements of subjectivity and objectivity (potentially) We’ll focus on both and delay much more discussion of interpretations until a bit further down the road Probability theory, strangely enough, can be developed rather fully without paying attention to interpretation Probability

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Introduction to Probability Probability Theory Interpretations Sample Spaces, Events Who cares? Why is it important to study probability?
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l1 - Outline Probability Probability Outline Outline 1...

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