PPT-Frequentist vs. Bayesian Estimation

CSE 6363 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. g Gaussian so only the parameters eg mean and variance need to be estimated Maximum Likelihood Bayesian Estimation Non parametric density estimation Assume NO knowledge about the density Kernel Density Estimation Nearest Neighbor Rule brPage 3br CSC 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 Frequentist Bayesian Fullinformation iteratedltering(mif) PMCMC(pmcmc) Feature-based nonlinearforecasting(nlf) ABC(abc) probematching&synthetic likelihood(probe.match) (b)Notplug-and-play Frequentist 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). Bayesian Network Motivation. We want a representation and reasoning system that is based on conditional . independence. Compact yet expressive representation. Efficient reasoning procedures. Bayesian Networks are such a representation. 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.. Author: David Heckerman. . Presented By:. Yan Zhang - 2006. Jeremy Gould – 2013. 1. Outline. Bayesian Approach. Bayesian vs. classical probability methods. Examples. Bayesian Network. Structure. Jun Zhang. , Graham . Cormode. , Cecilia M. . Procopiuc. , . Divesh. . Srivastava. , Xiaokui Xiao. The Problem: Private Data Release. Differential Privacy. Challenges. The Algorithm: PrivBayes. Bayesian Network. Week 9 and Week 10. 1. Announcement. Midterm II. 4/15. Scope. Data . warehousing and data cube. Neural . network. Open book. Project progress report. 4/22. 2. Team Homework Assignment #11. Read pp. 311 – 314.. Ha Le and Nikolaos Sarafianos. COSC 7362 – Advanced Machine Learning. Professor: Dr. Christoph F. . Eick. 1. Contents. Introduction. Dataset. Parametric Methods. Non-Parametric Methods. Evaluation. Using Stata. Chuck . Huber. StataCorp. chuber@stata.com. 2017 Canadian Stata Users Group Meeting. Bank of Canada, Ottawa. June 9, 2017. Introduction to . the . bayes. Prefix. in Stata 15. Chuck . Huber. Aakriti. Sharma and Pragya Adhikari. Bacterial . spot is one of the most important diseases of tomato in . North Carolina . and many other States, caused by multiple bacterial species and physiological races within the genus . In this class we will review . how statistics are used to . summarize data, special probability distributions, . their . use in simple applications using Frequentist and Bayesian . methods, and Monte Carlo techniques. Dr. Saadia Rashid Tariq. Quantitative estimation of copper (II), calcium (II) and chloride from a mixture. In this experiment the chloride ion is separated by precipitation with silver nitrate and estimated. Whereas copper(II) is estimated by iodometric titration and Calcium by complexometric titration .