PPT-Bayesian Reasoning Chapters 12 & 13

Thomas Bayes 17011761 151 2 Today s topics Motivation Review probability theory Bayesian inference From the joint distribution Using independencefactoring From sources of evidence Naïve Bayes algorithm for inference and classification tasks. De64257nition A Bayesian nonparametric model is a Bayesian model on an in64257nitedimensional parameter space The parameter space is typically chosen as the set of all possi ble solutions for a given learning problem For example in a regression prob P(. A . &. B. ) . = . P(. A. |. B. ) * P(. B. ). Product Rule:. Bayesian Reasoning. P(. A . &. B. ) . = . P(. A. |. B. ) * P(. B. ). Product Rule:. Shorthand for . . P(A=true & B=true) = P(A=true | B=true) * P(B=true). Read R&N Ch. 14.1-14.2. Next lecture: Read R&N 18.1-18.4. You will be expected to know. Basic concepts and vocabulary of Bayesian networks.. Nodes represent random variables.. Directed arcs represent (informally) direct influences.. Chris . Mathys. Wellcome Trust Centre for Neuroimaging. UCL. SPM Course (M/EEG). London, May 14, 2013. Thanks to Jean . Daunizeau. and . Jérémie. . Mattout. for previous versions of this talk. A spectacular piece of information. - Charles Sanders Peirce. Using Models of Reasoning. A Return to Logos. Reasoning from Specific Instances. Progressing from a number of particular facts to a general conclusion. .. This is also known as inductive reasoning.. Jun Zhang. , Graham . Cormode. , Cecilia M. . Procopiuc. , . Divesh. . Srivastava. , Xiaokui Xiao. The Problem: Private Data Release. Differential Privacy. Challenges. The Algorithm: PrivBayes. Bayesian Network. Henrik Singmann. A girl had NOT had sexual intercourse.. How likely is it that the girl is NOT pregnant?. A girl is NOT pregnant. . How likely is it that the girl had NOT had sexual intercourse?. A girl is pregnant. . or. How to combine data, evidence, opinion and guesstimates to make decisions. Information Technology. Professor Ann Nicholson. Faculty of Information Technology. Monash University . (Melbourne, Australia). Byron Smith. December 11, 2013. What is Quantum State Tomography?. What is Bayesian Statistics?. Conditional Probabilities. Bayes. ’ Rule. Frequentist. vs. Bayesian. Example: . Schrodinger’s Cat. Inference implemented on . FPGA. with . Stochastic . Bitstreams. for an Autonomous Robot . Jorge Lobo. jlobo@isr.uc.pt. Bayesian Inference implemented on FPGA. with Stochastic . Bitstreams. for an Autonomous Robot . CSE . 4309 . – Machine Learning. Vassilis. . Athitsos. Computer Science and Engineering Department. University of Texas at . Arlington. 1. Estimating Probabilities. In order to use probabilities, we need to estimate them.. Carrie Deis. Nadine Dewdney. Phase I clinical trials. Standard Designs. Adaptive Designs. Bayesian Approach. Traditional vs. Bayesian. Hybridization. FDA Guidance. Conclusion. Overview. Conducted to determine toxicity for the dosing of the new intervention. - Charles Sanders Peirce. On the Radar. Researching the Persuasive Speech Assignment. Due Wednesday on . WebCT. (by 11:59 p.m.). Exam Two. This Friday in Lecture. Study Guide on Course Website. Workshops for the Persuasive Speech. Cognitive Science. Current Problem:. . How do children learn and how do they get it right?. Connectionists and Associationists. Associationism:. . maintains that all knowledge is represented in terms of associations between ideas, that complex ideas are built up from combinations of more primitive ideas, which, in accordance with empiricist philosophy, are ultimately derived from the senses. .