D_+2010+Chapter+1 - 1 Introduction Probabilistic analysis...

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Chapter 1 CHIU © 1.1 1 Introduction P robabilistic analysis is about making sense of uncertainty. People are better equipped to interpret and compare alternatives in a deterministic environment. Uncertainty throws a curve, resulting in erroneous reasoning/intuition and misleading/murky communications. Intuition in an uncertain world can be trained aided by a rigorous framework to avoid common pitfalls, which is the intent of probabilistic analysis. You have been throwing heads in the last 10 coin flips, it is very likely that the next toss will be tails as the law of average will soon catch up with you. The next one has to be mine as I have been waiting long enough. – a waiting passenger at the luggage carousel. They are just guesses. They are possibilities, not probabilities. – Donald Rumsfeld dismissing potential dire scenarios in Iraq. O.J. Simpson was declared not guilty by the jury for the murder of his wife. Is he guilty or not? Probabilistic analysis aims to shed light on many seemingly ambiguous situations with the construction of a mathematical model. The following topical coverage is typical in an introductory probability class: sample space, random variables, distributions, expectation, conditional probability, independence, brand-name random variables, Law of Large Numbers, Central Limit Theorem, and estimation theory -- constituting the core focus of such classes. While this set of topics is essential to quantify uncertainties, they tend to highlight mathematical constructs while lacking motivation/intuition and problem formulation opportunities. We intend to place equal emphasis in problem formulation to complement mathematical analysis. A mathematical model provides a constructive venue agreeing on what to disagree. The following framing of "why", "what", and "how" of probabilistic analysis defines the orientation of this book. Why? Because we want: To understand uncertainties. To provide clarity to communicate uncertainties. To effectively use probabilistic information to enhance decision quality. To know how new probabilistic information can modify our state of knowledge. What (to do)? To build an axiomatic based mathematical model with an effective procedure to specify model components: what are possible and how likely. What (to do with the completed model)? To compute relevant/useful probabilistic quantities. To update probability using new information. To devise various metrics and representations useful for effective communications and to assist decision making. How? By creating principles and concepts, both fundamental and derived. By introducing procedures and technology (rules and tools).
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This note was uploaded on 09/28/2010 for the course MS&E 220 taught by Professor Chiu during the Fall '10 term at Stanford.

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D_+2010+Chapter+1 - 1 Introduction Probabilistic analysis...

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