Jump to content

File:MultivariateNormal.png

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (842 × 637 pixels, file size: 159 KB, MIME type: image/png)

Summary

Description
English: Illustration of a multivariate gaussian distribution and its marginals. Matlab code provided below.
Date
Source Own work
Author Bscan
%This script illustrates a multivariate Gaussian distribution and its
%marginal distributions

%This code is issued under the CC0 "license"

%Define limits of plotting
X = -5:0.1:5;
Y = -5:0.1:5;

%2-d Mean and covariance matrix
MeanVec = [0 0];
CovMatrix = [1 0.6; 0.6 2];

%Get the 1-d PDFs for the "walls"
Z_x = normpdf(X,MeanVec(1), sqrt(CovMatrix(1,1)));
Z_y = normpdf(Y,MeanVec(2), sqrt(CovMatrix(2,2)));

%Get the 2-d samples for the "floor"
Samples = mvnrnd(MeanVec, CovMatrix, 10000);

%Get the sigma ellipses by transform a circle by the cholesky decomp
L = chol(CovMatrix,'lower');
t = linspace(0,2*pi,100); %Our ellipse will have 100 points on it
C = [cos(t) ; sin(t)]; %A unit circle
E1 = 1*L*C; E2 = 2*L*C; E3 = 3*L*C; %Get the 1,2, and 3-sigma ellipses

figure; hold on; 
%Plot the samples on the "floor"
plot3(Samples(:,1),Samples(:,2),zeros(size(Samples,1),1),'k.','MarkerSize',2)
%Plot the 1,2, and 3-sigma ellipses slightly above the floor
%plot3(E1(1,:), E1(2,:), 1e-3+zeros(1,size(E1,2)),'Color','g','LineWidth',2);
%plot3(E2(1,:), E2(2,:), 1e-3+zeros(1,size(E2,2)),'Color','g','LineWidth',2);
plot3(E3(1,:), E3(2,:), 1e-3+zeros(1,size(E3,2)),'Color','g','LineWidth',2);

%Plot the histograms on the walls from the data in the middle
[n_x, xout] = hist(Samples(:,1),20);%Creates 20 bars
n_x = n_x ./ ( sum(n_x) *(xout(2)-xout(1)));%Normalizes to be a pdf
[~,~,~,x_Pos,x_Height] = makebars(xout,n_x);%Creates the bar points
plot3(x_Pos, Y(end)*ones(size(x_Pos)),x_Height,'-k')

%Now plot the other histograms on the wall
[n_y, yout] = hist(Samples(:,2),20);
n_y = n_y ./ ( sum(n_y) *(yout(2)-yout(1)));
[~,~,~,y_Pos,y_Height] = makebars(yout,n_y);
plot3(X(1)*ones(size(y_Pos)),y_Pos, y_Height,'-k')

%Now plot the 1-d pdfs over the histograms
plot3(X, ones(size(X))*Y(end), Z_x,'-b','LineWidth',2); 
plot3(ones(size(Y))*X(1), Y, Z_y,'-r','LineWidth',2);

%Make the figure look nice
grid on; view(45,55);
axis([X(1) X(end) Y(1) Y(end)])

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

22 March 2013

image/png

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current19:30, 22 March 2013Thumbnail for version as of 19:30, 22 March 2013842 × 637 (159 KB)BscanUser created page with UploadWizard

Global file usage

The following other wikis use this file:

Metadata