Estimating Gaussian noise model given a set of linear transformation
$begingroup$
I've done this stuff in a while.
Suppose we have a system of the form
$$
left{
begin{array}{l}
tilde{x}_1 = x_1 + epsilon_1 \
vdots \
tilde{x}_i = x_i + epsilon_i \
vdots \
tilde{x}_n = x_n + epsilon_n
end{array}
right.
$$
where each $epsilon_i$ is some value sampled from a distribution $mathcal{N}(mu,sigma)$
I've these measures $tilde{x}_i$s not related to the same quantity, but all the $epsilon_i$ are sampled from the same distribution. Is there any way I can possibly estimate the probability distribution (namely $mu,sigma$)?
Thank you
probability statistics
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
$endgroup$
add a comment |
$begingroup$
I've done this stuff in a while.
Suppose we have a system of the form
$$
left{
begin{array}{l}
tilde{x}_1 = x_1 + epsilon_1 \
vdots \
tilde{x}_i = x_i + epsilon_i \
vdots \
tilde{x}_n = x_n + epsilon_n
end{array}
right.
$$
where each $epsilon_i$ is some value sampled from a distribution $mathcal{N}(mu,sigma)$
I've these measures $tilde{x}_i$s not related to the same quantity, but all the $epsilon_i$ are sampled from the same distribution. Is there any way I can possibly estimate the probability distribution (namely $mu,sigma$)?
Thank you
probability statistics
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
$endgroup$
$begingroup$
What do we know about the $x_i$ ? Known distribution ? Fixed values ?
$endgroup$
– Damien
Jan 15 at 10:44
$begingroup$
@Damien, they're fixed/constants.
$endgroup$
– user8469759
Jan 15 at 10:50
$begingroup$
In this case, I don't understand where the problem is. By removing the $x_i$ from the observations, you get the $epsilon_i$. Estimating the mean and variance from these corrected observations seem simple. On the contrary, if they are fixed but unknown (classical case in communications), we need more information on it.
$endgroup$
– Damien
Jan 15 at 13:05
$begingroup$
They're fixed and unknown, except they're constants.
$endgroup$
– user8469759
Jan 15 at 13:09
add a comment |
$begingroup$
I've done this stuff in a while.
Suppose we have a system of the form
$$
left{
begin{array}{l}
tilde{x}_1 = x_1 + epsilon_1 \
vdots \
tilde{x}_i = x_i + epsilon_i \
vdots \
tilde{x}_n = x_n + epsilon_n
end{array}
right.
$$
where each $epsilon_i$ is some value sampled from a distribution $mathcal{N}(mu,sigma)$
I've these measures $tilde{x}_i$s not related to the same quantity, but all the $epsilon_i$ are sampled from the same distribution. Is there any way I can possibly estimate the probability distribution (namely $mu,sigma$)?
Thank you
probability statistics
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
$endgroup$
I've done this stuff in a while.
Suppose we have a system of the form
$$
left{
begin{array}{l}
tilde{x}_1 = x_1 + epsilon_1 \
vdots \
tilde{x}_i = x_i + epsilon_i \
vdots \
tilde{x}_n = x_n + epsilon_n
end{array}
right.
$$
where each $epsilon_i$ is some value sampled from a distribution $mathcal{N}(mu,sigma)$
I've these measures $tilde{x}_i$s not related to the same quantity, but all the $epsilon_i$ are sampled from the same distribution. Is there any way I can possibly estimate the probability distribution (namely $mu,sigma$)?
Thank you
probability statistics
probability statistics
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
asked Jan 15 at 9:59
user8469759user8469759
1,5731618
1,5731618
$begingroup$
What do we know about the $x_i$ ? Known distribution ? Fixed values ?
$endgroup$
– Damien
Jan 15 at 10:44
$begingroup$
@Damien, they're fixed/constants.
$endgroup$
– user8469759
Jan 15 at 10:50
$begingroup$
In this case, I don't understand where the problem is. By removing the $x_i$ from the observations, you get the $epsilon_i$. Estimating the mean and variance from these corrected observations seem simple. On the contrary, if they are fixed but unknown (classical case in communications), we need more information on it.
$endgroup$
– Damien
Jan 15 at 13:05
$begingroup$
They're fixed and unknown, except they're constants.
$endgroup$
– user8469759
Jan 15 at 13:09
add a comment |
$begingroup$
What do we know about the $x_i$ ? Known distribution ? Fixed values ?
$endgroup$
– Damien
Jan 15 at 10:44
$begingroup$
@Damien, they're fixed/constants.
$endgroup$
– user8469759
Jan 15 at 10:50
$begingroup$
In this case, I don't understand where the problem is. By removing the $x_i$ from the observations, you get the $epsilon_i$. Estimating the mean and variance from these corrected observations seem simple. On the contrary, if they are fixed but unknown (classical case in communications), we need more information on it.
$endgroup$
– Damien
Jan 15 at 13:05
$begingroup$
They're fixed and unknown, except they're constants.
$endgroup$
– user8469759
Jan 15 at 13:09
$begingroup$
What do we know about the $x_i$ ? Known distribution ? Fixed values ?
$endgroup$
– Damien
Jan 15 at 10:44
$begingroup$
What do we know about the $x_i$ ? Known distribution ? Fixed values ?
$endgroup$
– Damien
Jan 15 at 10:44
$begingroup$
@Damien, they're fixed/constants.
$endgroup$
– user8469759
Jan 15 at 10:50
$begingroup$
@Damien, they're fixed/constants.
$endgroup$
– user8469759
Jan 15 at 10:50
$begingroup$
In this case, I don't understand where the problem is. By removing the $x_i$ from the observations, you get the $epsilon_i$. Estimating the mean and variance from these corrected observations seem simple. On the contrary, if they are fixed but unknown (classical case in communications), we need more information on it.
$endgroup$
– Damien
Jan 15 at 13:05
$begingroup$
In this case, I don't understand where the problem is. By removing the $x_i$ from the observations, you get the $epsilon_i$. Estimating the mean and variance from these corrected observations seem simple. On the contrary, if they are fixed but unknown (classical case in communications), we need more information on it.
$endgroup$
– Damien
Jan 15 at 13:05
$begingroup$
They're fixed and unknown, except they're constants.
$endgroup$
– user8469759
Jan 15 at 13:09
$begingroup$
They're fixed and unknown, except they're constants.
$endgroup$
– user8469759
Jan 15 at 13:09
add a comment |
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$begingroup$
What do we know about the $x_i$ ? Known distribution ? Fixed values ?
$endgroup$
– Damien
Jan 15 at 10:44
$begingroup$
@Damien, they're fixed/constants.
$endgroup$
– user8469759
Jan 15 at 10:50
$begingroup$
In this case, I don't understand where the problem is. By removing the $x_i$ from the observations, you get the $epsilon_i$. Estimating the mean and variance from these corrected observations seem simple. On the contrary, if they are fixed but unknown (classical case in communications), we need more information on it.
$endgroup$
– Damien
Jan 15 at 13:05
$begingroup$
They're fixed and unknown, except they're constants.
$endgroup$
– user8469759
Jan 15 at 13:09