Show that the function is symmetric.
$begingroup$
Consider the following proposal function
$q(vec{theta'}|vec{theta})$:
For a given vector $vec{theta}=(theta_1,theta_2,theta_3)$
generate $vec{theta'}=(theta_1',theta_2',theta_3')$ as
$$theta_1'=|theta_1+delta_1|$$ $$theta_2'=|theta_2+delta_2|$$
$$theta_3'=|theta_3+delta_3|$$
where $delta_isim N(0,0.1^2).$ Show that the proposal function is
symmetric, i.e, that $q(vec{theta'}|vec{theta}) =
q(vec{theta}|vec{theta'}).$
I have that
$$q(vec{theta'}|vec{theta}) = q(|vec{theta} + vec{delta}|)$$
but when I try to calculate $q(vec{theta}|vec{theta'})$ I find that I need to solve $vec{theta}$ from $vec{theta'}=|vec{theta}+vec{delta}|.$ Am I missing something here?
probability probability-theory
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
$endgroup$
add a comment |
$begingroup$
Consider the following proposal function
$q(vec{theta'}|vec{theta})$:
For a given vector $vec{theta}=(theta_1,theta_2,theta_3)$
generate $vec{theta'}=(theta_1',theta_2',theta_3')$ as
$$theta_1'=|theta_1+delta_1|$$ $$theta_2'=|theta_2+delta_2|$$
$$theta_3'=|theta_3+delta_3|$$
where $delta_isim N(0,0.1^2).$ Show that the proposal function is
symmetric, i.e, that $q(vec{theta'}|vec{theta}) =
q(vec{theta}|vec{theta'}).$
I have that
$$q(vec{theta'}|vec{theta}) = q(|vec{theta} + vec{delta}|)$$
but when I try to calculate $q(vec{theta}|vec{theta'})$ I find that I need to solve $vec{theta}$ from $vec{theta'}=|vec{theta}+vec{delta}|.$ Am I missing something here?
probability probability-theory
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
$endgroup$
add a comment |
$begingroup$
Consider the following proposal function
$q(vec{theta'}|vec{theta})$:
For a given vector $vec{theta}=(theta_1,theta_2,theta_3)$
generate $vec{theta'}=(theta_1',theta_2',theta_3')$ as
$$theta_1'=|theta_1+delta_1|$$ $$theta_2'=|theta_2+delta_2|$$
$$theta_3'=|theta_3+delta_3|$$
where $delta_isim N(0,0.1^2).$ Show that the proposal function is
symmetric, i.e, that $q(vec{theta'}|vec{theta}) =
q(vec{theta}|vec{theta'}).$
I have that
$$q(vec{theta'}|vec{theta}) = q(|vec{theta} + vec{delta}|)$$
but when I try to calculate $q(vec{theta}|vec{theta'})$ I find that I need to solve $vec{theta}$ from $vec{theta'}=|vec{theta}+vec{delta}|.$ Am I missing something here?
probability probability-theory
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
$endgroup$
Consider the following proposal function
$q(vec{theta'}|vec{theta})$:
For a given vector $vec{theta}=(theta_1,theta_2,theta_3)$
generate $vec{theta'}=(theta_1',theta_2',theta_3')$ as
$$theta_1'=|theta_1+delta_1|$$ $$theta_2'=|theta_2+delta_2|$$
$$theta_3'=|theta_3+delta_3|$$
where $delta_isim N(0,0.1^2).$ Show that the proposal function is
symmetric, i.e, that $q(vec{theta'}|vec{theta}) =
q(vec{theta}|vec{theta'}).$
I have that
$$q(vec{theta'}|vec{theta}) = q(|vec{theta} + vec{delta}|)$$
but when I try to calculate $q(vec{theta}|vec{theta'})$ I find that I need to solve $vec{theta}$ from $vec{theta'}=|vec{theta}+vec{delta}|.$ Am I missing something here?
probability probability-theory
probability probability-theory
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
asked Dec 6 '18 at 15:53
ParsevalParseval
2,8751718
2,8751718
add a comment |
add a comment |
0
active
oldest
votes
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%2f3028666%2fshow-that-the-function-is-symmetric%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3028666%2fshow-that-the-function-is-symmetric%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
