Existence of a joint distribution given the conditional and marginal distributionJoint Distribution Not Obvious Algebraically for Graphical Modelsfind conditional probability from marginal probabilityBayesian inference of the true prior distribution, given posterior distributionMeasure theoretic basis of joint distrib of parameters and data in Bayesian analysisWhy if we use independence and factorization, we cannot represent every joint distribution? (rigorous argument needed)Marginal Distributions from Joint DistributionJoint probability distribution from all conditionals. Why is it not possible?Joint distribution of two normal marginal distributionsHow to construct a joint distribution given a continuous space?Proving that the conditional probability of a continuous distribution on a discrete distribution taking a value in a given interval is an integral
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Existence of a joint distribution given the conditional and marginal distribution
Joint Distribution Not Obvious Algebraically for Graphical Modelsfind conditional probability from marginal probabilityBayesian inference of the true prior distribution, given posterior distributionMeasure theoretic basis of joint distrib of parameters and data in Bayesian analysisWhy if we use independence and factorization, we cannot represent every joint distribution? (rigorous argument needed)Marginal Distributions from Joint DistributionJoint probability distribution from all conditionals. Why is it not possible?Joint distribution of two normal marginal distributionsHow to construct a joint distribution given a continuous space?Proving that the conditional probability of a continuous distribution on a discrete distribution taking a value in a given interval is an integral
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Can anyone point me a book where it has a proof of Theorem 1.7 (ii) of Jun Shao's book - Mathematical Statistics? I need this to show that given a distribution on one space and a collection of conditional distributions (which are conditioned on values of the first space) on another space, I can construct a joint distribution in the product space.
There is a print of the theorem below.
probability probability-theory probability-distributions statistical-inference conditional-probability
asked Mar 21 at 12:42
Ga13Ga13
5012
$endgroup$
add a comment |
$begingroup$
Can anyone point me a book where it has a proof of Theorem 1.7 (ii) of Jun Shao's book - Mathematical Statistics? I need this to show that given a distribution on one space and a collection of conditional distributions (which are conditioned on values of the first space) on another space, I can construct a joint distribution in the product space.
There is a print of the theorem below.
probability probability-theory probability-distributions statistical-inference conditional-probability
asked Mar 21 at 12:42
Ga13Ga13
5012
$endgroup$
$begingroup$
It seems to be a direct application of Carathéodory's extension theorem.
$endgroup$
– Saad
Mar 25 at 15:46
$begingroup$
I don't think so. I'm looking for a result that guarantees the existence of the joint distribution, since I have a conditional and marginal distribution.
$endgroup$
– Ga13
Mar 25 at 16:27
add a comment |
$begingroup$
Can anyone point me a book where it has a proof of Theorem 1.7 (ii) of Jun Shao's book - Mathematical Statistics? I need this to show that given a distribution on one space and a collection of conditional distributions (which are conditioned on values of the first space) on another space, I can construct a joint distribution in the product space.
There is a print of the theorem below.
probability probability-theory probability-distributions statistical-inference conditional-probability
asked Mar 21 at 12:42
Ga13Ga13
5012
$endgroup$
Can anyone point me a book where it has a proof of Theorem 1.7 (ii) of Jun Shao's book - Mathematical Statistics? I need this to show that given a distribution on one space and a collection of conditional distributions (which are conditioned on values of the first space) on another space, I can construct a joint distribution in the product space.
There is a print of the theorem below.
probability probability-theory probability-distributions statistical-inference conditional-probability
probability probability-theory probability-distributions statistical-inference conditional-probability
asked Mar 21 at 12:42
Ga13Ga13
5012
asked Mar 21 at 12:42
Ga13Ga13
5012
edited Mar 21 at 13:45
Ga13
asked Mar 21 at 12:42
Ga13Ga13
5012
asked Mar 21 at 12:42
Ga13Ga13
5012
asked Mar 21 at 12:42
Ga13Ga13
5012
5012
$begingroup$
It seems to be a direct application of Carathéodory's extension theorem.
$endgroup$
– Saad
Mar 25 at 15:46
$begingroup$
I don't think so. I'm looking for a result that guarantees the existence of the joint distribution, since I have a conditional and marginal distribution.
$endgroup$
– Ga13
Mar 25 at 16:27
add a comment |
$begingroup$
It seems to be a direct application of Carathéodory's extension theorem.
$endgroup$
– Saad
Mar 25 at 15:46
$begingroup$
I don't think so. I'm looking for a result that guarantees the existence of the joint distribution, since I have a conditional and marginal distribution.
$endgroup$
– Ga13
Mar 25 at 16:27
$begingroup$
It seems to be a direct application of Carathéodory's extension theorem.
$endgroup$
– Saad
Mar 25 at 15:46
$begingroup$
It seems to be a direct application of Carathéodory's extension theorem.
$endgroup$
– Saad
Mar 25 at 15:46
$begingroup$
I don't think so. I'm looking for a result that guarantees the existence of the joint distribution, since I have a conditional and marginal distribution.
$endgroup$
– Ga13
Mar 25 at 16:27
$begingroup$
I don't think so. I'm looking for a result that guarantees the existence of the joint distribution, since I have a conditional and marginal distribution.
$endgroup$
– Ga13
Mar 25 at 16:27
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
After much searching, I found the result that I needed. The theorem with the necessary proof is in the book: "Measure, Integration and Probability" from Burril, pages 397 - 399. (T.15-3C and T.15-3D)
answered Mar 28 at 15:35
Ga13Ga13
5012
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
After much searching, I found the result that I needed. The theorem with the necessary proof is in the book: "Measure, Integration and Probability" from Burril, pages 397 - 399. (T.15-3C and T.15-3D)
answered Mar 28 at 15:35
Ga13Ga13
5012
$endgroup$
add a comment |
$begingroup$
After much searching, I found the result that I needed. The theorem with the necessary proof is in the book: "Measure, Integration and Probability" from Burril, pages 397 - 399. (T.15-3C and T.15-3D)
answered Mar 28 at 15:35
Ga13Ga13
5012
$endgroup$
add a comment |
$begingroup$
After much searching, I found the result that I needed. The theorem with the necessary proof is in the book: "Measure, Integration and Probability" from Burril, pages 397 - 399. (T.15-3C and T.15-3D)
answered Mar 28 at 15:35
Ga13Ga13
5012
$endgroup$
After much searching, I found the result that I needed. The theorem with the necessary proof is in the book: "Measure, Integration and Probability" from Burril, pages 397 - 399. (T.15-3C and T.15-3D)
answered Mar 28 at 15:35
Ga13Ga13
5012
answered Mar 28 at 15:35
Ga13Ga13
5012
answered Mar 28 at 15:35
Ga13Ga13
5012
answered Mar 28 at 15:35
Ga13Ga13
5012
5012
add a comment |
add a comment |
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$begingroup$
It seems to be a direct application of Carathéodory's extension theorem.
$endgroup$
– Saad
Mar 25 at 15:46
$begingroup$
I don't think so. I'm looking for a result that guarantees the existence of the joint distribution, since I have a conditional and marginal distribution.
$endgroup$
– Ga13
Mar 25 at 16:27