Mixing
What is the difference between conditional probability and a stochastic kernel?
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I have visited various sites which claim a difference between stochastic kernels and conditional probability. However, I have read a paper which treats them the same, and the Wikipedia page on transition matrices actually lists a matrix full of conditional probabilities. The page linking to it claims that a Markov-kernel (stochastic-kernel, or probability-kernel) is simply an element of this transition matrix.
This is a contradiction in literature, and I would like some clarity on
the issue. What is the difference between a stochastic kernel and a
conditional probability statement?
It's possible they differ in generality alone, where the stochastic kernel is a specific case of conditional probability, but I haven't found any references on this.
probability-theory reference-request stochastic-processes
asked Jan 24 at 0:00
user400188user400188
4241614
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add a comment |
$begingroup$
I have visited various sites which claim a difference between stochastic kernels and conditional probability. However, I have read a paper which treats them the same, and the Wikipedia page on transition matrices actually lists a matrix full of conditional probabilities. The page linking to it claims that a Markov-kernel (stochastic-kernel, or probability-kernel) is simply an element of this transition matrix.
This is a contradiction in literature, and I would like some clarity on
the issue. What is the difference between a stochastic kernel and a
conditional probability statement?
It's possible they differ in generality alone, where the stochastic kernel is a specific case of conditional probability, but I haven't found any references on this.
probability-theory reference-request stochastic-processes
asked Jan 24 at 0:00
user400188user400188
4241614
$endgroup$
1
$begingroup$
The term "conditional probability" is general and context free, while "stochastic kernels" is used only when discussing stochastic processes. A stochastic kernel is a specific type of conditional probability (density) statement, while a conditional probability can be a statement that has nothing to do with stochastic processes.
$endgroup$
– Lee David Chung Lin
Jan 24 at 0:38
add a comment |
$begingroup$
I have visited various sites which claim a difference between stochastic kernels and conditional probability. However, I have read a paper which treats them the same, and the Wikipedia page on transition matrices actually lists a matrix full of conditional probabilities. The page linking to it claims that a Markov-kernel (stochastic-kernel, or probability-kernel) is simply an element of this transition matrix.
This is a contradiction in literature, and I would like some clarity on
the issue. What is the difference between a stochastic kernel and a
conditional probability statement?
It's possible they differ in generality alone, where the stochastic kernel is a specific case of conditional probability, but I haven't found any references on this.
probability-theory reference-request stochastic-processes
asked Jan 24 at 0:00
user400188user400188
4241614
$endgroup$
I have visited various sites which claim a difference between stochastic kernels and conditional probability. However, I have read a paper which treats them the same, and the Wikipedia page on transition matrices actually lists a matrix full of conditional probabilities. The page linking to it claims that a Markov-kernel (stochastic-kernel, or probability-kernel) is simply an element of this transition matrix.
This is a contradiction in literature, and I would like some clarity on
the issue. What is the difference between a stochastic kernel and a
conditional probability statement?
It's possible they differ in generality alone, where the stochastic kernel is a specific case of conditional probability, but I haven't found any references on this.
probability-theory reference-request stochastic-processes
probability-theory reference-request stochastic-processes
asked Jan 24 at 0:00
user400188user400188
4241614
asked Jan 24 at 0:00
user400188user400188
4241614
asked Jan 24 at 0:00
user400188user400188
4241614
asked Jan 24 at 0:00
user400188user400188
4241614
asked Jan 24 at 0:00
user400188user400188
4241614
4241614
1
$begingroup$
The term "conditional probability" is general and context free, while "stochastic kernels" is used only when discussing stochastic processes. A stochastic kernel is a specific type of conditional probability (density) statement, while a conditional probability can be a statement that has nothing to do with stochastic processes.
$endgroup$
– Lee David Chung Lin
Jan 24 at 0:38
add a comment |
1
$begingroup$
The term "conditional probability" is general and context free, while "stochastic kernels" is used only when discussing stochastic processes. A stochastic kernel is a specific type of conditional probability (density) statement, while a conditional probability can be a statement that has nothing to do with stochastic processes.
$endgroup$
– Lee David Chung Lin
Jan 24 at 0:38
1
1
$begingroup$
The term "conditional probability" is general and context free, while "stochastic kernels" is used only when discussing stochastic processes. A stochastic kernel is a specific type of conditional probability (density) statement, while a conditional probability can be a statement that has nothing to do with stochastic processes.
$endgroup$
– Lee David Chung Lin
Jan 24 at 0:38
$begingroup$
The term "conditional probability" is general and context free, while "stochastic kernels" is used only when discussing stochastic processes. A stochastic kernel is a specific type of conditional probability (density) statement, while a conditional probability can be a statement that has nothing to do with stochastic processes.
$endgroup$
– Lee David Chung Lin
Jan 24 at 0:38
add a comment |
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$begingroup$
The term "conditional probability" is general and context free, while "stochastic kernels" is used only when discussing stochastic processes. A stochastic kernel is a specific type of conditional probability (density) statement, while a conditional probability can be a statement that has nothing to do with stochastic processes.
$endgroup$
– Lee David Chung Lin
Jan 24 at 0:38