Probability Notation for p(x, theta|X) with Bayes theorem
I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
asked Jan 2 at 20:24
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
asked Jan 2 at 20:24
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
asked Jan 2 at 20:24
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
probability probability-distributions
asked Jan 2 at 20:24
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 2 at 20:24
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 2 at 20:24
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 2 at 20:24
tmptplayer
1011
asked Jan 2 at 20:24
tmptplayer
1011
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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
});
}
});
tmptplayer is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3059935%2fprobability-notation-for-px-thetax-with-bayes-theorem%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
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 4 at 0:32
tmptplayer
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 4 at 0:32
tmptplayer
1011
answered Jan 4 at 0:32
tmptplayer
1011
1011
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
tmptplayer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
tmptplayer is a new contributor. Be nice, and check out our Code of Conduct.
tmptplayer is a new contributor. Be nice, and check out our Code of Conduct.
tmptplayer is a new contributor. Be nice, and check out our Code of Conduct.
tmptplayer is a new contributor. Be nice, and check out our Code of Conduct.
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3059935%2fprobability-notation-for-px-thetax-with-bayes-theorem%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
