Bayesian interpretation of product distribution?
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I am reading this article about product distribution and I am reading it because of bayesian part, but unfortunately I can not understand part of this part (https://en.wikipedia.org/wiki/Product_distribution#A_Bayesian_Interpretation).
What operation is made to result from: "Letting $ theta $ be a random variable with pdf $ f_theta (theta) $, the distribution of the scaled sample becomes $$ f_X (theta X) = g_X (X | theta) f_theta (theta) dtheta $$ ? Where $ dtheta $ comes from?
probability-theory probability-distributions bayesian bayes-theorem
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
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add a comment |
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I am reading this article about product distribution and I am reading it because of bayesian part, but unfortunately I can not understand part of this part (https://en.wikipedia.org/wiki/Product_distribution#A_Bayesian_Interpretation).
What operation is made to result from: "Letting $ theta $ be a random variable with pdf $ f_theta (theta) $, the distribution of the scaled sample becomes $$ f_X (theta X) = g_X (X | theta) f_theta (theta) dtheta $$ ? Where $ dtheta $ comes from?
probability-theory probability-distributions bayesian bayes-theorem
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
$endgroup$
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It's a typo - the next thing that's defined is $h_x(x) = int_{-infty}^{infty} g_x(x mid theta) f_theta(theta) d theta$ and the $d theta$ must have got copied over for some reason. I've corrected it on the page.
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– Alex
Dec 26 '18 at 10:41
add a comment |
$begingroup$
I am reading this article about product distribution and I am reading it because of bayesian part, but unfortunately I can not understand part of this part (https://en.wikipedia.org/wiki/Product_distribution#A_Bayesian_Interpretation).
What operation is made to result from: "Letting $ theta $ be a random variable with pdf $ f_theta (theta) $, the distribution of the scaled sample becomes $$ f_X (theta X) = g_X (X | theta) f_theta (theta) dtheta $$ ? Where $ dtheta $ comes from?
probability-theory probability-distributions bayesian bayes-theorem
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
$endgroup$
I am reading this article about product distribution and I am reading it because of bayesian part, but unfortunately I can not understand part of this part (https://en.wikipedia.org/wiki/Product_distribution#A_Bayesian_Interpretation).
What operation is made to result from: "Letting $ theta $ be a random variable with pdf $ f_theta (theta) $, the distribution of the scaled sample becomes $$ f_X (theta X) = g_X (X | theta) f_theta (theta) dtheta $$ ? Where $ dtheta $ comes from?
probability-theory probability-distributions bayesian bayes-theorem
probability-theory probability-distributions bayesian bayes-theorem
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
asked Dec 23 '18 at 7:51
koralgoollkoralgooll
504
504
$begingroup$
It's a typo - the next thing that's defined is $h_x(x) = int_{-infty}^{infty} g_x(x mid theta) f_theta(theta) d theta$ and the $d theta$ must have got copied over for some reason. I've corrected it on the page.
$endgroup$
– Alex
Dec 26 '18 at 10:41
add a comment |
$begingroup$
It's a typo - the next thing that's defined is $h_x(x) = int_{-infty}^{infty} g_x(x mid theta) f_theta(theta) d theta$ and the $d theta$ must have got copied over for some reason. I've corrected it on the page.
$endgroup$
– Alex
Dec 26 '18 at 10:41
$begingroup$
It's a typo - the next thing that's defined is $h_x(x) = int_{-infty}^{infty} g_x(x mid theta) f_theta(theta) d theta$ and the $d theta$ must have got copied over for some reason. I've corrected it on the page.
$endgroup$
– Alex
Dec 26 '18 at 10:41
$begingroup$
It's a typo - the next thing that's defined is $h_x(x) = int_{-infty}^{infty} g_x(x mid theta) f_theta(theta) d theta$ and the $d theta$ must have got copied over for some reason. I've corrected it on the page.
$endgroup$
– Alex
Dec 26 '18 at 10:41
add a comment |
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$begingroup$
It's a typo - the next thing that's defined is $h_x(x) = int_{-infty}^{infty} g_x(x mid theta) f_theta(theta) d theta$ and the $d theta$ must have got copied over for some reason. I've corrected it on the page.
$endgroup$
– Alex
Dec 26 '18 at 10:41