Positive and negative precision error correlations, real or not?
All the experiments we have been carrying out with precision error have, so far, been with real data. Because of this, we do not have “ground truth” to determine if the reconstruction is correct. That changed today.
Synthetic experiments are a well-known device for studying models or algorithms. By artificially creating data where one knows exactly what is going on, one can then see if the algorithm one is testing is able to reproduce the artificially created “ground truth”.
I did that today by creating an artificial landscape as shown in the left figure at the top. A single example from the ten noisy versions of this landscape is shown in the figure on the right.
The advantage of using precision error is shown in the figures at the bottom. The figure on the left shows what happens after weighting the maps with the discovered precision error covariance matrix. The picture on the right is the result of simple averaging. The difference is clear. The weighted average is better, and precision error estimation was the way to obtain the weights.
