Surface Plot of Multivariate Normal Density
I have a likelihood function with Multivariate Normal Density whose mean is mu=[3 5]' and covariance=9*I. How can I plot its 2D surface in Matlab?
matlab normal-distribution probability-density
edited Feb 27 at 7:44
SecretAgentMan
718316
asked Nov 27 '18 at 23:14
john greenjohn green
11
add a comment |
I have a likelihood function with Multivariate Normal Density whose mean is mu=[3 5]' and covariance=9*I. How can I plot its 2D surface in Matlab?
matlab normal-distribution probability-density
edited Feb 27 at 7:44
SecretAgentMan
718316
asked Nov 27 '18 at 23:14
john greenjohn green
11
add a comment |
I have a likelihood function with Multivariate Normal Density whose mean is mu=[3 5]' and covariance=9*I. How can I plot its 2D surface in Matlab?
matlab normal-distribution probability-density
edited Feb 27 at 7:44
SecretAgentMan
718316
asked Nov 27 '18 at 23:14
john greenjohn green
11
I have a likelihood function with Multivariate Normal Density whose mean is mu=[3 5]' and covariance=9*I. How can I plot its 2D surface in Matlab?
matlab normal-distribution probability-density
matlab normal-distribution probability-density
edited Feb 27 at 7:44
SecretAgentMan
718316
asked Nov 27 '18 at 23:14
john greenjohn green
11
edited Feb 27 at 7:44
SecretAgentMan
718316
asked Nov 27 '18 at 23:14
john greenjohn green
11
edited Feb 27 at 7:44
SecretAgentMan
718316
edited Feb 27 at 7:44
SecretAgentMan
718316
edited Feb 27 at 7:44
SecretAgentMan
718316
718316
asked Nov 27 '18 at 23:14
john greenjohn green
11
asked Nov 27 '18 at 23:14
john greenjohn green
11
asked Nov 27 '18 at 23:14
john greenjohn green
11
11
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
The log-likelihood function can be obtained from the PDF or by referencing the wiki.
Mu = [3 5]';
Sigma = 9*eye(2);
loglikeh=@(x) -0.5*log(det(Sigma)) + (x-Mu)'*inv(Sigma)*(x-Mu) + length(x)*log(2*pi); % For single x
xMin = -2;
xMax = 7;
step = 0.1;
X1 = xMin:step:xMax;
X2 = xMin:step:xMax;
L = zeros(length(X1),length(X2));
for i = 1:length(X1)
for j = 1:length(X2)
x = [X1(i) X2(j)]';
L(i,j) = loglikeh(x);
end
end
If I've made a mistake, please comment so I can fix. Hope this helps.
Plotting
surf(X1,X2,L') % Note L is transposed if done this way
xlabel('x_1')
ylabel('x_2')
zlabel('log-likelihood')
See these answers for more visualizations and options.
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
add a comment |
You may try to refer in here:
(use mvnpdf function in MATLAB)
F = mvnpdf([X1(:) X2(:)],mu,Sigma)
Please check here https://www.mathworks.com/help/stats/multivariate-normal-distribution.html
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
The multivariate Normal probability density function (PDF) and likelihood function are not the same thing. See here
– SecretAgentMan
Nov 28 '18 at 14:55
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
The log-likelihood function can be obtained from the PDF or by referencing the wiki.
Mu = [3 5]';
Sigma = 9*eye(2);
loglikeh=@(x) -0.5*log(det(Sigma)) + (x-Mu)'*inv(Sigma)*(x-Mu) + length(x)*log(2*pi); % For single x
xMin = -2;
xMax = 7;
step = 0.1;
X1 = xMin:step:xMax;
X2 = xMin:step:xMax;
L = zeros(length(X1),length(X2));
for i = 1:length(X1)
for j = 1:length(X2)
x = [X1(i) X2(j)]';
L(i,j) = loglikeh(x);
end
end
If I've made a mistake, please comment so I can fix. Hope this helps.
Plotting
surf(X1,X2,L') % Note L is transposed if done this way
xlabel('x_1')
ylabel('x_2')
zlabel('log-likelihood')
See these answers for more visualizations and options.
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
add a comment |
The log-likelihood function can be obtained from the PDF or by referencing the wiki.
Mu = [3 5]';
Sigma = 9*eye(2);
loglikeh=@(x) -0.5*log(det(Sigma)) + (x-Mu)'*inv(Sigma)*(x-Mu) + length(x)*log(2*pi); % For single x
xMin = -2;
xMax = 7;
step = 0.1;
X1 = xMin:step:xMax;
X2 = xMin:step:xMax;
L = zeros(length(X1),length(X2));
for i = 1:length(X1)
for j = 1:length(X2)
x = [X1(i) X2(j)]';
L(i,j) = loglikeh(x);
end
end
If I've made a mistake, please comment so I can fix. Hope this helps.
Plotting
surf(X1,X2,L') % Note L is transposed if done this way
xlabel('x_1')
ylabel('x_2')
zlabel('log-likelihood')
See these answers for more visualizations and options.
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
add a comment |
The log-likelihood function can be obtained from the PDF or by referencing the wiki.
Mu = [3 5]';
Sigma = 9*eye(2);
loglikeh=@(x) -0.5*log(det(Sigma)) + (x-Mu)'*inv(Sigma)*(x-Mu) + length(x)*log(2*pi); % For single x
xMin = -2;
xMax = 7;
step = 0.1;
X1 = xMin:step:xMax;
X2 = xMin:step:xMax;
L = zeros(length(X1),length(X2));
for i = 1:length(X1)
for j = 1:length(X2)
x = [X1(i) X2(j)]';
L(i,j) = loglikeh(x);
end
end
If I've made a mistake, please comment so I can fix. Hope this helps.
Plotting
surf(X1,X2,L') % Note L is transposed if done this way
xlabel('x_1')
ylabel('x_2')
zlabel('log-likelihood')
See these answers for more visualizations and options.
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
The log-likelihood function can be obtained from the PDF or by referencing the wiki.
Mu = [3 5]';
Sigma = 9*eye(2);
loglikeh=@(x) -0.5*log(det(Sigma)) + (x-Mu)'*inv(Sigma)*(x-Mu) + length(x)*log(2*pi); % For single x
xMin = -2;
xMax = 7;
step = 0.1;
X1 = xMin:step:xMax;
X2 = xMin:step:xMax;
L = zeros(length(X1),length(X2));
for i = 1:length(X1)
for j = 1:length(X2)
x = [X1(i) X2(j)]';
L(i,j) = loglikeh(x);
end
end
If I've made a mistake, please comment so I can fix. Hope this helps.
Plotting
surf(X1,X2,L') % Note L is transposed if done this way
xlabel('x_1')
ylabel('x_2')
zlabel('log-likelihood')
See these answers for more visualizations and options.
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
answered Nov 28 '18 at 15:13
SecretAgentManSecretAgentMan
718316
718316
add a comment |
add a comment |
You may try to refer in here:
(use mvnpdf function in MATLAB)
F = mvnpdf([X1(:) X2(:)],mu,Sigma)
Please check here https://www.mathworks.com/help/stats/multivariate-normal-distribution.html
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
The multivariate Normal probability density function (PDF) and likelihood function are not the same thing. See here
– SecretAgentMan
Nov 28 '18 at 14:55
add a comment |
You may try to refer in here:
(use mvnpdf function in MATLAB)
F = mvnpdf([X1(:) X2(:)],mu,Sigma)
Please check here https://www.mathworks.com/help/stats/multivariate-normal-distribution.html
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
The multivariate Normal probability density function (PDF) and likelihood function are not the same thing. See here
– SecretAgentMan
Nov 28 '18 at 14:55
add a comment |
You may try to refer in here:
(use mvnpdf function in MATLAB)
F = mvnpdf([X1(:) X2(:)],mu,Sigma)
Please check here https://www.mathworks.com/help/stats/multivariate-normal-distribution.html
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
You may try to refer in here:
(use mvnpdf function in MATLAB)
F = mvnpdf([X1(:) X2(:)],mu,Sigma)
Please check here https://www.mathworks.com/help/stats/multivariate-normal-distribution.html
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
answered Nov 28 '18 at 1:10
A. SyamA. Syam
113119
113119
The multivariate Normal probability density function (PDF) and likelihood function are not the same thing. See here
– SecretAgentMan
Nov 28 '18 at 14:55
add a comment |
The multivariate Normal probability density function (PDF) and likelihood function are not the same thing. See here
– SecretAgentMan
Nov 28 '18 at 14:55
The multivariate Normal probability density function (PDF) and likelihood function are not the same thing. See here
– SecretAgentMan
Nov 28 '18 at 14:55
The multivariate Normal probability density function (PDF) and likelihood function are not the same thing. See here
– SecretAgentMan
Nov 28 '18 at 14:55
add a comment |
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