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
Assassin's bullet with mercury
How to prevent "they're falling in love" trope
Can one be a co-translator of a book, if he does not know the language that the book is translated into?
Why doesn't H₄O²⁺ exist?
What exploit are these user agents trying to use?
What reasons are there for a Capitalist to oppose a 100% inheritance tax?
Stopping power of mountain vs road bike
Can a virus destroy the BIOS of a modern computer?
Twin primes whose sum is a cube
What is the intuition behind short exact sequences of groups; in particular, what is the intuition behind group extensions?
Blender 2.8 I can't see vertices, edges or faces in edit mode
Is there a hemisphere-neutral way of specifying a season?
What to put in ESTA if staying in US for a few days before going on to Canada
Infinite Abelian subgroup of infinite non Abelian group example
How can saying a song's name be a copyright violation?
Fully-Firstable Anagram Sets
Today is the Center
Is it possible to run Internet Explorer on OS X El Capitan?
Is Lorentz symmetry broken if SUSY is broken?
SSH "lag" in LAN on some machines, mixed distros
How do I write bicross product symbols in latex?
Is it inappropriate for a student to attend their mentor's dissertation defense?
I'm flying to France today and my passport expires in less than 2 months
Why does Arabsat 6A need a Falcon Heavy to launch
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
$begingroup$
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
$endgroup$
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 |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3156777%2fexistence-of-a-joint-distribution-given-the-conditional-and-marginal-distributio%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
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 |
$begingroup$
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 |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3156777%2fexistence-of-a-joint-distribution-given-the-conditional-and-marginal-distributio%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
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