Transcription of Chapter 13 The Multivariate Gaussian - People
{{id}} {{{paragraph}}}
Example: confidence
Chapter 13 The Multivariate Gaussian - People
Chapter 13 The Multivariate GaussianIn this Chapter we present some basic facts regarding the Multivariate Gaussian discuss the two major parameterizations of the Multivariate Gaussian themomentparameterizationand thecanonical parameterization, and we show how the basic operationsof marginalization and conditioning are carried out in thesetwo parameterizations. We alsodiscuss maximum likelihood estimation for the Multivariate ParameterizationsThe Multivariate Gaussian distribution is commonly expressed interms of the parameters and , where is ann 1 vector and is ann n, symmetric matrix. (We will assumefor now that is also positive definite, but later on we will haveoccasion to relax thatconstraint). We have the following form for the density function:p(x| , ) =1(2 )n/2| |1/2exp{ 12(x )T 1(x )},( )wherexis a vector in n. The density can be integrated over volumes in nto assignprobability mass to those geometry of the Multivariate Gaussian is essentially that associated with the quadraticformf(x) =12(x )T 1(x ) in the exponent of the density.
2 CHAPTER 13. THE MULTIVARIATE GAUSSIAN The factor in front of the exponential in Eq. 13.1 is the normalization factor that ensures that the density integrates to one.
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
Related search queries
Chapter 5. Multivariate Probability Distributions, Multivariate probability, Probability, Chapter 3 Multivariate Probability, Chapter 3 Multivariate Probability 3, Chapter 2 Multivariate Distributions, Multivariate, 730 Chapter 3: Normal Distribution Theory, Chapter, 3 Random vectors and multivariate normal distribution, Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 3, Introduction to Probability and, Chapter 2 Multivariate Distributions and Transformations, Introduction to Probability and Statistics, Univariate Probability