Thread: CRT offsets View Single Post 2021-04-06, 16:06   #19
CraigLo

Mar 2021

53 Posts Quote:
 Originally Posted by henryzz @CraigLo How are you working out your probabilities? The obvious calculation is to sum the probabilities for each start point x < 0 that a gap >=xx merit starts there. However, these probabilities don't strike me as independent so summing them wouldn't be correct. I assume that this calculation is always going to be too slow to optimize based on this.

1. Calculate the probability that a gap >= G starts at the first point < 0.
2. Calculate the probability that a gap >= G starts at the second point < 0. A gap starting here will also include the first point so add this to the probability for the first point as well.
3. Calculate the probability that a gap >= G starts at the third point < 0. A gap starting here will also include the first and second points so add this to the probability for the first two as well.
4. Continue this for all points < 0.

When you are finished we have the probability that a point is included in a gap >= G. Every gap will include the first point. A gap will include a point at G/2 only about half the time so sieving a point at G/2 is only half as helpful as sieving a point at 0. A gap will only include a point at 3G/4 about 1/10th the time so sieving a point here is only 1/10th as helpful as sieving a point at 0.

The probabilities calculated above will change depending on the offset chosen but I think the changes will be small enough that they can be ignored. With this assumption the probabilities can be pre-computed and the optimization problem is similar to the one you are already doing.

You are currently subtracting 1 for each element sieved in the interval -G/2 to G/2 and 0 outside this region and minimizing the result.

I am suggesting we subtract the pre-computed probability for each element sieved over the interval -G to G and minimize this.  