Relating posterior to the least square estimator of W
up vote
1
down vote
favorite
I'm currently working on an assigment and I'm currently stuck and could really use some help, I've been given the fact that my prior over my parameters W is given by a gaussian pdf, likewise is the likelihood a gaussian pdf. Without any further proof the posterior can also be taken for a gaussian.
My expression for the posterior is:
$$p(textbf{W}vert textbf{X},textbf{T}) = exp(-frac{1}{2}textbf{W}^{T}Sigma_w^{-1}textbf{W} +textbf{W}^{T}Sigma_w^{-1}textbf{W}_mu -frac{1}{2}textbf{W}_mu^{T}Sigma_w^{-1}textbf{W}_mu)$$
I've made derivations for the mean $textbf{W}_mu$ and the covariance $Sigma_w^{-1}$, but I don't think they play an important role to what I'm supposed to do here. I think I should use maximum likelihood but I don't seem to get the calculations right.
normal-distribution maximum-likelihood
add a comment |
up vote
1
down vote
favorite
I'm currently working on an assigment and I'm currently stuck and could really use some help, I've been given the fact that my prior over my parameters W is given by a gaussian pdf, likewise is the likelihood a gaussian pdf. Without any further proof the posterior can also be taken for a gaussian.
My expression for the posterior is:
$$p(textbf{W}vert textbf{X},textbf{T}) = exp(-frac{1}{2}textbf{W}^{T}Sigma_w^{-1}textbf{W} +textbf{W}^{T}Sigma_w^{-1}textbf{W}_mu -frac{1}{2}textbf{W}_mu^{T}Sigma_w^{-1}textbf{W}_mu)$$
I've made derivations for the mean $textbf{W}_mu$ and the covariance $Sigma_w^{-1}$, but I don't think they play an important role to what I'm supposed to do here. I think I should use maximum likelihood but I don't seem to get the calculations right.
normal-distribution maximum-likelihood
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm currently working on an assigment and I'm currently stuck and could really use some help, I've been given the fact that my prior over my parameters W is given by a gaussian pdf, likewise is the likelihood a gaussian pdf. Without any further proof the posterior can also be taken for a gaussian.
My expression for the posterior is:
$$p(textbf{W}vert textbf{X},textbf{T}) = exp(-frac{1}{2}textbf{W}^{T}Sigma_w^{-1}textbf{W} +textbf{W}^{T}Sigma_w^{-1}textbf{W}_mu -frac{1}{2}textbf{W}_mu^{T}Sigma_w^{-1}textbf{W}_mu)$$
I've made derivations for the mean $textbf{W}_mu$ and the covariance $Sigma_w^{-1}$, but I don't think they play an important role to what I'm supposed to do here. I think I should use maximum likelihood but I don't seem to get the calculations right.
normal-distribution maximum-likelihood
I'm currently working on an assigment and I'm currently stuck and could really use some help, I've been given the fact that my prior over my parameters W is given by a gaussian pdf, likewise is the likelihood a gaussian pdf. Without any further proof the posterior can also be taken for a gaussian.
My expression for the posterior is:
$$p(textbf{W}vert textbf{X},textbf{T}) = exp(-frac{1}{2}textbf{W}^{T}Sigma_w^{-1}textbf{W} +textbf{W}^{T}Sigma_w^{-1}textbf{W}_mu -frac{1}{2}textbf{W}_mu^{T}Sigma_w^{-1}textbf{W}_mu)$$
I've made derivations for the mean $textbf{W}_mu$ and the covariance $Sigma_w^{-1}$, but I don't think they play an important role to what I'm supposed to do here. I think I should use maximum likelihood but I don't seem to get the calculations right.
normal-distribution maximum-likelihood
normal-distribution maximum-likelihood
edited yesterday
asked yesterday
A.Maine
448
448
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2996375%2frelating-posterior-to-the-least-square-estimator-of-w%23new-answer', 'question_page');
}
);
Post as a guest
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password