Probability Notation for p(x, theta|X) with Bayes theorem
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I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
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add a comment |
$begingroup$
I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
$endgroup$
add a comment |
$begingroup$
I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
$endgroup$
I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.
After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:
p(x |X ) = ∫p(x, θ |X )dθ
I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?
Thanks for the help!
probability probability-distributions
probability probability-distributions
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
asked Jan 2 at 20:24
tmptplayertmptplayer
1012
1012
add a comment |
add a comment |
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After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
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add a comment |
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$begingroup$
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
$endgroup$
add a comment |
$begingroup$
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
$endgroup$
add a comment |
$begingroup$
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
$endgroup$
After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
answered Jan 4 at 0:32
tmptplayertmptplayer
1012
1012
add a comment |
add a comment |
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