PDF-Chance and Uncertainty: Probability Theory Formally, we begin with a

A is mutually exclusive and exhaustive if each is disjoint from the others and together they cover all possibilities If A A are mutually exclusive and exhaustive then PrB PrB. Through this class we will be relying on concepts from probability theory for deriving machine learning algorithms These notes attempt to cover the basics of probability theory at a level appropriate for CS 229 The mathematical theory of probability Lack of knowledge vs. variability.. What type of safety measures do we take?. Design, manufacturing, operations & post-mortems. Living with uncertainties vs. changing them. How do we represent random variables?. Jake Blanchard. Spring 2010. Uncertainty Analysis for Engineers. 1. Introduction. Interpretations of Probability. Classical – If an event can occur in N equally likely and different ways, and if n of these have an attribute A, then the probability of the occurrence of A, denoted Pr(A), is defined as n/N. uncertainty assessment. in hydrological modelling. Alberto . Montanari. Department DICAM – University of Bologna. alberto.montanari@unibo.it. Premise: the problem is not new..... “. It seems to me that the condition of confidence or otherwise forms a very important part of the prediction, and ought to find expression. Predictability of Change. Alberto . Montanari. (1). and . Guenter. . Bloeschl. (2). (1) . University of Bologna, . alberto.montanari@unibo.it. (2) . Vienna University of Technology, . bloeschl@hydro.tuwien.ac.at. Lars Thomsen, Avondale College . Re-. conceptualising. probability. What has changed?. Changes in the Probability Standard. Old 2.6. New 2.13. Simulation . Tree diagrams. (old Level 1 probability). Simulate probability situations. Making Uncertainty Valuable not Risky. About KCA. Management Consultancy focused on Energy, Technology, and Related Markets.. Work with clients to develop and implement game-changing strategies, improve operational efficiencies, and reduce costs through long-term competitive advantage.. “The . scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of very great importance, I think. . When . a scientist does not know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty damn sure of what the result is going to be, he is still in some doubt. . Decision. . Theory. Wolfgang Spohn. Multi-. disciplinary. . approaches. . to. . reasoning. . with. . imperfect. . information. . and. . knowledge. . – . a . synthesis. . and. a . roadmap. March 23, 2010. Outline. Intro & Definitions. Why learn about probabilities and risk?. What is learned?. Expected Utility. Prospect Theory. Scalar Utility Theory. Choices, choices, choices.... In the lab, reinforcement is often uniform. What is probability?. Classical definition:. the . ratio. of “favorable” to equally probable . cases. .. “. favorable”. :. . the kind you’re interested . in. .. Probability of getting heads on flipping a fair coin: 1/2 (heads is 1 of 2 possibilities). Assessing risk, . considering chances and uncertainties.. What is Probability?. “A strong likelihood or chance of something” (dictionary.com). “The likelihood of something occurring or the chance of something happening” (yourdictionary.com). Behavioral Economics. Udayan. Roy. Misconceptions over probabilities. Trouble Assessing Probabilities. People tend to make specific errors in assessing probabilities. Hot-hand fallacy. is the belief that once an event has occurred several times in a row it is . 4. Interpret probability as a long-run relative frequency. . Dispel . common myths about randomness.. Use . simulation to model chance behavior.. Randomness, Probability, and Simulation. Randomness, Probability, and Simulation.