Specification for Bayesian updating with flat prior
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I am reading a research paper that adopts Bayesian learning process or Bayesian updating, and I found it very confusing for me to understand the notation or specification used.
As I copy the paper, a person forms her belief or valuation, $v_{it}$, through,
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$,
where $hat{v_{it}}$ is a signal provided, which is drawn from $N(v_{it}, sigma^2_hat{v})$.
By doing this, the paper says that she gets an unbiased signal of their true valuation. In addition, the paper adds that this specification of beliefs arises when one has flat prior, or prior variance = $infty$ and processed the signal, $hat{v})$, according to Bayes' rule.
The point that I don't understand is that they use $v_{it}$ twice: they first seem to consider $v_{it}$ as a random variable, and then they use $v_{it}$ as if it is a parameter. So I wonder if I understand the context right. I also wonder if this is a conventional specification in Bayesian context. If not, what would be the intention of the author to use less conventional specification?
In addition if I change the specification as following, does this change the intention of the original specification?
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$, (same)
where $hat{v_{it}}$ is drawn from $N(tilde{v_{it}}, sigma^2_hat{v})$. (considering another notation for the true valuation, $tilde{v_{it}}$).
probability statistics bayesian bayes-theorem
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
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add a comment |
$begingroup$
I am reading a research paper that adopts Bayesian learning process or Bayesian updating, and I found it very confusing for me to understand the notation or specification used.
As I copy the paper, a person forms her belief or valuation, $v_{it}$, through,
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$,
where $hat{v_{it}}$ is a signal provided, which is drawn from $N(v_{it}, sigma^2_hat{v})$.
By doing this, the paper says that she gets an unbiased signal of their true valuation. In addition, the paper adds that this specification of beliefs arises when one has flat prior, or prior variance = $infty$ and processed the signal, $hat{v})$, according to Bayes' rule.
The point that I don't understand is that they use $v_{it}$ twice: they first seem to consider $v_{it}$ as a random variable, and then they use $v_{it}$ as if it is a parameter. So I wonder if I understand the context right. I also wonder if this is a conventional specification in Bayesian context. If not, what would be the intention of the author to use less conventional specification?
In addition if I change the specification as following, does this change the intention of the original specification?
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$, (same)
where $hat{v_{it}}$ is drawn from $N(tilde{v_{it}}, sigma^2_hat{v})$. (considering another notation for the true valuation, $tilde{v_{it}}$).
probability statistics bayesian bayes-theorem
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
$endgroup$
$begingroup$
Thank you for your help in advance!
$endgroup$
– J.Doe
Dec 6 '18 at 7:57
add a comment |
$begingroup$
I am reading a research paper that adopts Bayesian learning process or Bayesian updating, and I found it very confusing for me to understand the notation or specification used.
As I copy the paper, a person forms her belief or valuation, $v_{it}$, through,
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$,
where $hat{v_{it}}$ is a signal provided, which is drawn from $N(v_{it}, sigma^2_hat{v})$.
By doing this, the paper says that she gets an unbiased signal of their true valuation. In addition, the paper adds that this specification of beliefs arises when one has flat prior, or prior variance = $infty$ and processed the signal, $hat{v})$, according to Bayes' rule.
The point that I don't understand is that they use $v_{it}$ twice: they first seem to consider $v_{it}$ as a random variable, and then they use $v_{it}$ as if it is a parameter. So I wonder if I understand the context right. I also wonder if this is a conventional specification in Bayesian context. If not, what would be the intention of the author to use less conventional specification?
In addition if I change the specification as following, does this change the intention of the original specification?
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$, (same)
where $hat{v_{it}}$ is drawn from $N(tilde{v_{it}}, sigma^2_hat{v})$. (considering another notation for the true valuation, $tilde{v_{it}}$).
probability statistics bayesian bayes-theorem
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
$endgroup$
I am reading a research paper that adopts Bayesian learning process or Bayesian updating, and I found it very confusing for me to understand the notation or specification used.
As I copy the paper, a person forms her belief or valuation, $v_{it}$, through,
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$,
where $hat{v_{it}}$ is a signal provided, which is drawn from $N(v_{it}, sigma^2_hat{v})$.
By doing this, the paper says that she gets an unbiased signal of their true valuation. In addition, the paper adds that this specification of beliefs arises when one has flat prior, or prior variance = $infty$ and processed the signal, $hat{v})$, according to Bayes' rule.
The point that I don't understand is that they use $v_{it}$ twice: they first seem to consider $v_{it}$ as a random variable, and then they use $v_{it}$ as if it is a parameter. So I wonder if I understand the context right. I also wonder if this is a conventional specification in Bayesian context. If not, what would be the intention of the author to use less conventional specification?
In addition if I change the specification as following, does this change the intention of the original specification?
$v_{it}$ ~ $N(hat{v_{it}},sigma^2_hat{v})$, (same)
where $hat{v_{it}}$ is drawn from $N(tilde{v_{it}}, sigma^2_hat{v})$. (considering another notation for the true valuation, $tilde{v_{it}}$).
probability statistics bayesian bayes-theorem
probability statistics bayesian bayes-theorem
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
asked Dec 6 '18 at 7:56
J.DoeJ.Doe
1
1
$begingroup$
Thank you for your help in advance!
$endgroup$
– J.Doe
Dec 6 '18 at 7:57
add a comment |
$begingroup$
Thank you for your help in advance!
$endgroup$
– J.Doe
Dec 6 '18 at 7:57
$begingroup$
Thank you for your help in advance!
$endgroup$
– J.Doe
Dec 6 '18 at 7:57
$begingroup$
Thank you for your help in advance!
$endgroup$
– J.Doe
Dec 6 '18 at 7:57
add a comment |
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Thank you for your help in advance!
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– J.Doe
Dec 6 '18 at 7:57