EE - 613 : Probabilistic Generative Models , lab 2 Fall 2015 1 Maximum - A - Posteriori adaptation of a multivariate Gaussian

  • Published 2015

Abstract

The goal is to study the estimation of the parameters (μ,Σ) using the Maximum A Posteriori (MAP) principle. Comparison with the Maximum-Likelihood estimator and the effect of the prior parameters will be studied. Let’s assume that we are give a set of i.i.d. observations X = {xi, i = 1 . . . N} that follow a multivariate Gaussian law N (x|μ,Σ), where the data points are of dimension d. It has been shown that the conjugate prior for the parameter (μ,Σ) of this multivariate Gaussian likelihood distribution is the Normal-Inverse Wishart distribution: p(μ,Σ|m, τ, V, ν) = NIW(μ,Σ|β) = NIW(μ,Σ|m, τ, V, ν) = p(μ|Σ,m, τ)p(Σ|V, ν) (1)

1 Figure or Table

Cite this paper

@inproceedings{2015EE6, title={EE - 613 : Probabilistic Generative Models , lab 2 Fall 2015 1 Maximum - A - Posteriori adaptation of a multivariate Gaussian}, author={}, year={2015} }