MAP estimator - Computation Solution
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MAP estimator - Computation Solution
$begingroup$
I am developing a MAP estimator for my problem. I need to know how to calculate my estimation when my pdf is not a known form (like Gaussian). I hope there is an efficient numerical way to do this. After a background of my problem, I ask my questions in two separate parts.
A little background: I deal with a life time estimation for electronic devices. For a given device under test, I process sensory data(D) and convert them to samples of possible life time for that device. Let's say the lifetime is a random variable (like X) and I have samples of its postier given sensory Data (i.e P(x|D)). Now I like to use argmax of P(x|D) as my final estimation for lifetime. Unfortunately, P(x|D) varies from case to case and I can't assume a fixed distribution family for it like Gaussian and it does not conform a specific known form.
Now Questions:
Q1) (Simple way) Is there any efficient numerical method for calculating the argmax of P(x|D) using its samples? (I can imagine doing it in two steps, like first fitting a pdf using something like parzen then solving an optimization for finding its max, but this does not sound very efficient).
Q2) (More Advanced) Let's say for each sample from postior, I have a weight factor showing some sort of level of uncertainty about that sample. (For e.g. we can think of a measurement noise in samples and this weight shows the variance of the additive noise.) Is there anyway that I can include this weight (of uncertainty level) in my estimator?
Please, cite any reference you know.
Thanks
probability parameter-estimation graphical-model estimators expectation-maximization
asked 1 min ago
KatiKati
1
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am developing a MAP estimator for my problem. I need to know how to calculate my estimation when my pdf is not a known form (like Gaussian). I hope there is an efficient numerical way to do this. After a background of my problem, I ask my questions in two separate parts.
A little background: I deal with a life time estimation for electronic devices. For a given device under test, I process sensory data(D) and convert them to samples of possible life time for that device. Let's say the lifetime is a random variable (like X) and I have samples of its postier given sensory Data (i.e P(x|D)). Now I like to use argmax of P(x|D) as my final estimation for lifetime. Unfortunately, P(x|D) varies from case to case and I can't assume a fixed distribution family for it like Gaussian and it does not conform a specific known form.
Now Questions:
Q1) (Simple way) Is there any efficient numerical method for calculating the argmax of P(x|D) using its samples? (I can imagine doing it in two steps, like first fitting a pdf using something like parzen then solving an optimization for finding its max, but this does not sound very efficient).
Q2) (More Advanced) Let's say for each sample from postior, I have a weight factor showing some sort of level of uncertainty about that sample. (For e.g. we can think of a measurement noise in samples and this weight shows the variance of the additive noise.) Is there anyway that I can include this weight (of uncertainty level) in my estimator?
Please, cite any reference you know.
Thanks
probability parameter-estimation graphical-model estimators expectation-maximization
asked 1 min ago
KatiKati
1
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am developing a MAP estimator for my problem. I need to know how to calculate my estimation when my pdf is not a known form (like Gaussian). I hope there is an efficient numerical way to do this. After a background of my problem, I ask my questions in two separate parts.
A little background: I deal with a life time estimation for electronic devices. For a given device under test, I process sensory data(D) and convert them to samples of possible life time for that device. Let's say the lifetime is a random variable (like X) and I have samples of its postier given sensory Data (i.e P(x|D)). Now I like to use argmax of P(x|D) as my final estimation for lifetime. Unfortunately, P(x|D) varies from case to case and I can't assume a fixed distribution family for it like Gaussian and it does not conform a specific known form.
Now Questions:
Q1) (Simple way) Is there any efficient numerical method for calculating the argmax of P(x|D) using its samples? (I can imagine doing it in two steps, like first fitting a pdf using something like parzen then solving an optimization for finding its max, but this does not sound very efficient).
Q2) (More Advanced) Let's say for each sample from postior, I have a weight factor showing some sort of level of uncertainty about that sample. (For e.g. we can think of a measurement noise in samples and this weight shows the variance of the additive noise.) Is there anyway that I can include this weight (of uncertainty level) in my estimator?
Please, cite any reference you know.
Thanks
probability parameter-estimation graphical-model estimators expectation-maximization
asked 1 min ago
KatiKati
1
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am developing a MAP estimator for my problem. I need to know how to calculate my estimation when my pdf is not a known form (like Gaussian). I hope there is an efficient numerical way to do this. After a background of my problem, I ask my questions in two separate parts.
A little background: I deal with a life time estimation for electronic devices. For a given device under test, I process sensory data(D) and convert them to samples of possible life time for that device. Let's say the lifetime is a random variable (like X) and I have samples of its postier given sensory Data (i.e P(x|D)). Now I like to use argmax of P(x|D) as my final estimation for lifetime. Unfortunately, P(x|D) varies from case to case and I can't assume a fixed distribution family for it like Gaussian and it does not conform a specific known form.
Now Questions:
Q1) (Simple way) Is there any efficient numerical method for calculating the argmax of P(x|D) using its samples? (I can imagine doing it in two steps, like first fitting a pdf using something like parzen then solving an optimization for finding its max, but this does not sound very efficient).
Q2) (More Advanced) Let's say for each sample from postior, I have a weight factor showing some sort of level of uncertainty about that sample. (For e.g. we can think of a measurement noise in samples and this weight shows the variance of the additive noise.) Is there anyway that I can include this weight (of uncertainty level) in my estimator?
Please, cite any reference you know.
Thanks
probability parameter-estimation graphical-model estimators expectation-maximization
probability parameter-estimation graphical-model estimators expectation-maximization
asked 1 min ago
KatiKati
1
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 min ago
KatiKati
1
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 min ago
KatiKati
1
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 min ago
KatiKati
1
asked 1 min ago
KatiKati
1
1
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Kati is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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