Why is the Beta distribution used as a prior distribution in this problem?
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Let $theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes as an answer. Then an appropriate statistical model for this problem will be the geometric distribution.
Now suppose that we perform the survey again in $2018$ expecting that the proportion of $theta$ obtained in $2017$ remains the same. Then we assume the following prior distribution $text{Beta}(ktheta,k(1-theta))$ where $k$ is some constant, say equal to $5.$ Then I want to understand why using this prior distribution makes sense for this situation.
I read that the beta distribution is the conjugate prior to the geometric distribution but the parameters here are quite different. So maybe there is something else that I am missing.
I also wanted to know if the following is true: the proportion $p$ for the survey is now a random variable such that
$$psim text{Beta}(ktheta,k(1-theta)).$$
Then $mathbb{P}[p=x|theta] =frac{1}{beta(ktheta,k-ktheta)}cdot x^{ktheta-1}(1-x)^{k(1-theta)-1}.$
statistics bayesian
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
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add a comment |
$begingroup$
Let $theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes as an answer. Then an appropriate statistical model for this problem will be the geometric distribution.
Now suppose that we perform the survey again in $2018$ expecting that the proportion of $theta$ obtained in $2017$ remains the same. Then we assume the following prior distribution $text{Beta}(ktheta,k(1-theta))$ where $k$ is some constant, say equal to $5.$ Then I want to understand why using this prior distribution makes sense for this situation.
I read that the beta distribution is the conjugate prior to the geometric distribution but the parameters here are quite different. So maybe there is something else that I am missing.
I also wanted to know if the following is true: the proportion $p$ for the survey is now a random variable such that
$$psim text{Beta}(ktheta,k(1-theta)).$$
Then $mathbb{P}[p=x|theta] =frac{1}{beta(ktheta,k-ktheta)}cdot x^{ktheta-1}(1-x)^{k(1-theta)-1}.$
statistics bayesian
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
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Please do not cross-post.
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– StubbornAtom
Jan 2 at 6:50
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I don't think it was the right forum for my question. How do I transfer my question to this forum?
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– model_checker
Jan 2 at 7:04
add a comment |
$begingroup$
Let $theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes as an answer. Then an appropriate statistical model for this problem will be the geometric distribution.
Now suppose that we perform the survey again in $2018$ expecting that the proportion of $theta$ obtained in $2017$ remains the same. Then we assume the following prior distribution $text{Beta}(ktheta,k(1-theta))$ where $k$ is some constant, say equal to $5.$ Then I want to understand why using this prior distribution makes sense for this situation.
I read that the beta distribution is the conjugate prior to the geometric distribution but the parameters here are quite different. So maybe there is something else that I am missing.
I also wanted to know if the following is true: the proportion $p$ for the survey is now a random variable such that
$$psim text{Beta}(ktheta,k(1-theta)).$$
Then $mathbb{P}[p=x|theta] =frac{1}{beta(ktheta,k-ktheta)}cdot x^{ktheta-1}(1-x)^{k(1-theta)-1}.$
statistics bayesian
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
$endgroup$
Let $theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes as an answer. Then an appropriate statistical model for this problem will be the geometric distribution.
Now suppose that we perform the survey again in $2018$ expecting that the proportion of $theta$ obtained in $2017$ remains the same. Then we assume the following prior distribution $text{Beta}(ktheta,k(1-theta))$ where $k$ is some constant, say equal to $5.$ Then I want to understand why using this prior distribution makes sense for this situation.
I read that the beta distribution is the conjugate prior to the geometric distribution but the parameters here are quite different. So maybe there is something else that I am missing.
I also wanted to know if the following is true: the proportion $p$ for the survey is now a random variable such that
$$psim text{Beta}(ktheta,k(1-theta)).$$
Then $mathbb{P}[p=x|theta] =frac{1}{beta(ktheta,k-ktheta)}cdot x^{ktheta-1}(1-x)^{k(1-theta)-1}.$
statistics bayesian
statistics bayesian
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
asked Jan 2 at 6:06
model_checkermodel_checker
4,34121931
4,34121931
$begingroup$
Please do not cross-post.
$endgroup$
– StubbornAtom
Jan 2 at 6:50
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I don't think it was the right forum for my question. How do I transfer my question to this forum?
$endgroup$
– model_checker
Jan 2 at 7:04
add a comment |
$begingroup$
Please do not cross-post.
$endgroup$
– StubbornAtom
Jan 2 at 6:50
$begingroup$
I don't think it was the right forum for my question. How do I transfer my question to this forum?
$endgroup$
– model_checker
Jan 2 at 7:04
$begingroup$
Please do not cross-post.
$endgroup$
– StubbornAtom
Jan 2 at 6:50
$begingroup$
Please do not cross-post.
$endgroup$
– StubbornAtom
Jan 2 at 6:50
$begingroup$
I don't think it was the right forum for my question. How do I transfer my question to this forum?
$endgroup$
– model_checker
Jan 2 at 7:04
$begingroup$
I don't think it was the right forum for my question. How do I transfer my question to this forum?
$endgroup$
– model_checker
Jan 2 at 7:04
add a comment |
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$begingroup$
Please do not cross-post.
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– StubbornAtom
Jan 2 at 6:50
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I don't think it was the right forum for my question. How do I transfer my question to this forum?
$endgroup$
– model_checker
Jan 2 at 7:04