variance-based upper bound for entropy: proof? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Metric Entropy Upper BoundsShannon entropy property proofInfinite Discrete Form of Jensen's InequalityWhat should say the isoperimetric inequality for taxicab geometry?Entropy/Variance inequalityupper bound on logarithmic potentialHow to prove the inequality $frac4^m4sqrtmlebinom2mm$ using chebyshev inequalityHelp in understanding a proof in descriptive statisticsDiscrete version of Bihari-Lasalle inequalityUpper bound of Mutual Information
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variance-based upper bound for entropy: proof?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Metric Entropy Upper BoundsShannon entropy property proofInfinite Discrete Form of Jensen's InequalityWhat should say the isoperimetric inequality for taxicab geometry?Entropy/Variance inequalityupper bound on logarithmic potentialHow to prove the inequality $frac4^m4sqrtmlebinom2mm$ using chebyshev inequalityHelp in understanding a proof in descriptive statisticsDiscrete version of Bihari-Lasalle inequalityUpper bound of Mutual Information
$begingroup$
I found the inequality in wikipedia https://en.wikipedia.org/wiki/Entropic_uncertainty
$$
H(phi )leq log sqrt 2pi eV(phi ),
$$
with $phi$ as "any probability density function on the real line".
Can anyone point to the proof of this statement? What about discrete case?
inequality variance entropy
asked Mar 27 at 3:26
lowtechlowtech
1916
$endgroup$
add a comment |
$begingroup$
I found the inequality in wikipedia https://en.wikipedia.org/wiki/Entropic_uncertainty
$$
H(phi )leq log sqrt 2pi eV(phi ),
$$
with $phi$ as "any probability density function on the real line".
Can anyone point to the proof of this statement? What about discrete case?
inequality variance entropy
asked Mar 27 at 3:26
lowtechlowtech
1916
$endgroup$
$begingroup$
The proof is standard and available in wikipedia. In the discrete case, the entropy is upper bounded by $log M$, where $M$ is the number of possible values of the random variable.
$endgroup$
– Stelios
Mar 27 at 12:47
add a comment |
$begingroup$
I found the inequality in wikipedia https://en.wikipedia.org/wiki/Entropic_uncertainty
$$
H(phi )leq log sqrt 2pi eV(phi ),
$$
with $phi$ as "any probability density function on the real line".
Can anyone point to the proof of this statement? What about discrete case?
inequality variance entropy
asked Mar 27 at 3:26
lowtechlowtech
1916
$endgroup$
I found the inequality in wikipedia https://en.wikipedia.org/wiki/Entropic_uncertainty
$$
H(phi )leq log sqrt 2pi eV(phi ),
$$
with $phi$ as "any probability density function on the real line".
Can anyone point to the proof of this statement? What about discrete case?
inequality variance entropy
inequality variance entropy
asked Mar 27 at 3:26
lowtechlowtech
1916
asked Mar 27 at 3:26
lowtechlowtech
1916
edited Mar 27 at 3:49
lowtech
asked Mar 27 at 3:26
lowtechlowtech
1916
asked Mar 27 at 3:26
lowtechlowtech
1916
asked Mar 27 at 3:26
lowtechlowtech
1916
1916
$begingroup$
The proof is standard and available in wikipedia. In the discrete case, the entropy is upper bounded by $log M$, where $M$ is the number of possible values of the random variable.
$endgroup$
– Stelios
Mar 27 at 12:47
add a comment |
$begingroup$
The proof is standard and available in wikipedia. In the discrete case, the entropy is upper bounded by $log M$, where $M$ is the number of possible values of the random variable.
$endgroup$
– Stelios
Mar 27 at 12:47
$begingroup$
The proof is standard and available in wikipedia. In the discrete case, the entropy is upper bounded by $log M$, where $M$ is the number of possible values of the random variable.
$endgroup$
– Stelios
Mar 27 at 12:47
$begingroup$
The proof is standard and available in wikipedia. In the discrete case, the entropy is upper bounded by $log M$, where $M$ is the number of possible values of the random variable.
$endgroup$
– Stelios
Mar 27 at 12:47
add a comment |
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$begingroup$
The proof is standard and available in wikipedia. In the discrete case, the entropy is upper bounded by $log M$, where $M$ is the number of possible values of the random variable.
$endgroup$
– Stelios
Mar 27 at 12:47