Accept - Reject of Normal Distribution with prior Cauchy
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If $X sim N(theta,1)$ with Cauchy as robust prior
$$pi(theta) = frac{1}{pi(1+theta^2)} qquad -infty < theta < infty$$
how to do the rejection sampler in R, and use it to generate 10, 000 samples from the posterior distribution. with using R function 'rcauchy' to simulate from π(θ); $pi$($theta$) is a proposal distribution.
Kindly please help
bayesian
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
$endgroup$
add a comment |
$begingroup$
If $X sim N(theta,1)$ with Cauchy as robust prior
$$pi(theta) = frac{1}{pi(1+theta^2)} qquad -infty < theta < infty$$
how to do the rejection sampler in R, and use it to generate 10, 000 samples from the posterior distribution. with using R function 'rcauchy' to simulate from π(θ); $pi$($theta$) is a proposal distribution.
Kindly please help
bayesian
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
$endgroup$
$begingroup$
" r function rcauchy" needs clarification.
$endgroup$
– herb steinberg
Dec 8 '18 at 2:41
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Why do you need to use rejection sampling here? You can just generate $10{,}000$ samples ${theta_1, dots,theta_{10{,}000}}$ from the Cauchy distribution and then simulate ${X_1, dots, X_{10{,}000}}$ by simulating $X_i sim N(theta_i, 1)$.
$endgroup$
– Alex
Dec 16 '18 at 17:36
add a comment |
$begingroup$
If $X sim N(theta,1)$ with Cauchy as robust prior
$$pi(theta) = frac{1}{pi(1+theta^2)} qquad -infty < theta < infty$$
how to do the rejection sampler in R, and use it to generate 10, 000 samples from the posterior distribution. with using R function 'rcauchy' to simulate from π(θ); $pi$($theta$) is a proposal distribution.
Kindly please help
bayesian
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
$endgroup$
If $X sim N(theta,1)$ with Cauchy as robust prior
$$pi(theta) = frac{1}{pi(1+theta^2)} qquad -infty < theta < infty$$
how to do the rejection sampler in R, and use it to generate 10, 000 samples from the posterior distribution. with using R function 'rcauchy' to simulate from π(θ); $pi$($theta$) is a proposal distribution.
Kindly please help
bayesian
bayesian
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
edited Dec 8 '18 at 12:29
shuvam agrawal
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
asked Dec 8 '18 at 2:20
shuvam agrawalshuvam agrawal
12
12
$begingroup$
" r function rcauchy" needs clarification.
$endgroup$
– herb steinberg
Dec 8 '18 at 2:41
$begingroup$
Why do you need to use rejection sampling here? You can just generate $10{,}000$ samples ${theta_1, dots,theta_{10{,}000}}$ from the Cauchy distribution and then simulate ${X_1, dots, X_{10{,}000}}$ by simulating $X_i sim N(theta_i, 1)$.
$endgroup$
– Alex
Dec 16 '18 at 17:36
add a comment |
$begingroup$
" r function rcauchy" needs clarification.
$endgroup$
– herb steinberg
Dec 8 '18 at 2:41
$begingroup$
Why do you need to use rejection sampling here? You can just generate $10{,}000$ samples ${theta_1, dots,theta_{10{,}000}}$ from the Cauchy distribution and then simulate ${X_1, dots, X_{10{,}000}}$ by simulating $X_i sim N(theta_i, 1)$.
$endgroup$
– Alex
Dec 16 '18 at 17:36
$begingroup$
" r function rcauchy" needs clarification.
$endgroup$
– herb steinberg
Dec 8 '18 at 2:41
$begingroup$
" r function rcauchy" needs clarification.
$endgroup$
– herb steinberg
Dec 8 '18 at 2:41
$begingroup$
Why do you need to use rejection sampling here? You can just generate $10{,}000$ samples ${theta_1, dots,theta_{10{,}000}}$ from the Cauchy distribution and then simulate ${X_1, dots, X_{10{,}000}}$ by simulating $X_i sim N(theta_i, 1)$.
$endgroup$
– Alex
Dec 16 '18 at 17:36
$begingroup$
Why do you need to use rejection sampling here? You can just generate $10{,}000$ samples ${theta_1, dots,theta_{10{,}000}}$ from the Cauchy distribution and then simulate ${X_1, dots, X_{10{,}000}}$ by simulating $X_i sim N(theta_i, 1)$.
$endgroup$
– Alex
Dec 16 '18 at 17:36
add a comment |
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$begingroup$
" r function rcauchy" needs clarification.
$endgroup$
– herb steinberg
Dec 8 '18 at 2:41
$begingroup$
Why do you need to use rejection sampling here? You can just generate $10{,}000$ samples ${theta_1, dots,theta_{10{,}000}}$ from the Cauchy distribution and then simulate ${X_1, dots, X_{10{,}000}}$ by simulating $X_i sim N(theta_i, 1)$.
$endgroup$
– Alex
Dec 16 '18 at 17:36