Concave exponential distribution
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Given
$$Cov_{theta}{phi(x)}=nabla_{theta,theta}^{2}psi(theta)$$
ϕ stands for "the sufficient statistics" and ψ is the log-partition function which acts like a normalizer to make sure the pdf integrates to 1.
How can I conclude that the log-likelihood in $f_{theta}(x)$ is concave in the parameters $theta$?
probability-theory probability-distributions
asked Nov 16 at 16:20
Nickpick
1136
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up vote
0
down vote
favorite
Given
$$Cov_{theta}{phi(x)}=nabla_{theta,theta}^{2}psi(theta)$$
ϕ stands for "the sufficient statistics" and ψ is the log-partition function which acts like a normalizer to make sure the pdf integrates to 1.
How can I conclude that the log-likelihood in $f_{theta}(x)$ is concave in the parameters $theta$?
probability-theory probability-distributions
asked Nov 16 at 16:20
Nickpick
1136
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given
$$Cov_{theta}{phi(x)}=nabla_{theta,theta}^{2}psi(theta)$$
ϕ stands for "the sufficient statistics" and ψ is the log-partition function which acts like a normalizer to make sure the pdf integrates to 1.
How can I conclude that the log-likelihood in $f_{theta}(x)$ is concave in the parameters $theta$?
probability-theory probability-distributions
asked Nov 16 at 16:20
Nickpick
1136
Given
$$Cov_{theta}{phi(x)}=nabla_{theta,theta}^{2}psi(theta)$$
ϕ stands for "the sufficient statistics" and ψ is the log-partition function which acts like a normalizer to make sure the pdf integrates to 1.
How can I conclude that the log-likelihood in $f_{theta}(x)$ is concave in the parameters $theta$?
probability-theory probability-distributions
probability-theory probability-distributions
asked Nov 16 at 16:20
Nickpick
1136
asked Nov 16 at 16:20
Nickpick
1136
asked Nov 16 at 16:20
Nickpick
1136
asked Nov 16 at 16:20
Nickpick
1136
asked Nov 16 at 16:20
Nickpick
1136
1136
add a comment |
add a comment |
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