PPT-Reservoir modeling using Gaussian mixture models

2 Introduction Many linear inverse problems are solved using a Bayesian approach assuming Gaussian distribution of the model We show the analytical solution of the Bayesian linear inverse problem in the Gaussian mixture case. edu Ming Yuan mingyuanisyegatechedu School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta GA 30332 USA Hui Zou hzoustatumnedu School of Statistics University of Minnesota Minneapolis MN 55455 USA Finite gaussian mixture . Introduction . to Environmental . Engineering and Science. Readings for This Class:. 5.5-5.6. O. hio . N. orthern . U. niversity. Introduction. Chemistry, Microbiology & Material Balance. Water & Air Pollution. Marti Blad PhD PE. EPA Definitions. Dispersion Models. : Estimate pollutants at ground level receptors. Photochemical Models. : Estimate regional air quality, predicts chemical reactions. Receptor Models. Mikhail . Belkin. Dept. of Computer Science and Engineering, . Dept. of Statistics . Ohio State . University / ISTA. Joint work with . Kaushik. . Sinha. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . Alan Ritter. Latent Variable Models. Previously: learning parameters with fully observed data. Alternate approach: hidden (latent) variables. Latent Cause. Q: how do we learn parameters?. Unsupervised Learning. Mixture Models and Expectation Maximization. Machine Learning. Last Time. Review of Supervised Learning. Clustering. K-means. Soft K-means. Today. Gaussian Mixture Models. Expectation Maximization. The Problem. Machine Learning. April 13, 2010. Last Time. Review of Supervised Learning. Clustering. K-means. Soft K-means. Today. A brief look at Homework 2. Gaussian Mixture Models. Expectation Maximization. The Problem. Daniel Lee. Presentation for MMM conference . May 24, 2016. University of Connecticut. 1. 2. Introduction: Finite Mixture Models. Class of statistical models that treat group membership as a latent categorical variable. . A . Brief . Introduction. Image from Univ. of Waterloo Environmental Sciences. Marti Blad. 2. Transport of Air Pollution. Plumes tell story. Ambient . vs. DALR. Models predict air pollution concentrations . Jaehoon. Lee, . Tapan. . Mukerji. , Michael Tompkins. Motivation and Objective. 2. Joint integration of multidisciplinary geophysical data can provide complementary information not only in reservoir characterization but also in reservoir monitoring.. EPA Definitions. Dispersion Models. : Estimate pollutants at ground level receptors. Photochemical Models. : Estimate regional air quality, predicts chemical reactions. Receptor Models. : Estimate contribution of multiple sources to receptor location based on multiple measurements at receptor. Mikhail . Belkin. Dept. of Computer Science and Engineering, . Dept. of Statistics . Ohio State . University / ISTA. Joint work with . Kaushik. . Sinha. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . Trang Quynh Nguyen, May 9, 2016. 410.686.01 Advanced Quantitative Methods in the Social and Behavioral Sciences: A Practical Introduction. Objectives. Provide a QUICK introduction to latent class models and finite mixture modeling, with examples. the . EM Algorithm. CSE . 6363 – Machine Learning. Vassilis. . Athitsos. Computer Science and Engineering Department. University of Texas at . Arlington. 1. Gaussians. A popular way to estimate . probability density .