Relating posterior to the least square estimator of W
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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
asked Nov 13 at 6:09
A.Maine
448
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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
asked Nov 13 at 6:09
A.Maine
448
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
asked Nov 13 at 6:09
A.Maine
448
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
asked Nov 13 at 6:09
A.Maine
448
asked Nov 13 at 6:09
A.Maine
448
edited Nov 13 at 6:16
asked Nov 13 at 6:09
A.Maine
448
asked Nov 13 at 6:09
A.Maine
448
asked Nov 13 at 6:09
A.Maine
448
448
add a comment |
add a comment |
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