I have the following observation model : $y_i=x_i+a_i$, where $a_i$ is a Gaussian random variable whose mean is function of a uniform random variable $b_i$. I have designed, $\hat{x}_i$, an estimator of $x_i$ and would like to evaluate its performance using Monte-Carlo simulations. I use the following logic, which I appreciate if you can criticize:
For i=1:I
n=0
Generate an $x_i$ uniformly from a given distribution
for j=1:J
Generate $b_j$ as a r.v. from a given uniform distribution
for k=1:K
Generate $a_jk$ as a normal r.v. conditional to $b_j$
Generate synthetic data: $y_jk=x_i+a_jk$
Obtain $\hat{x}_n$ using $y_jk$
n++
end
end
find $\hat{x}_i$ as the average of $\hat{x}_n$
end
calculate the RMS of error.
Note that the distributions of $a$ and $b$ can be anything. However, I don't have access to the joint PDF's. Instead I have the following:
- The distribution of $x$
- The distribution of $b$
- The distribution of $a|b$