#261 FBR Colocalisation costes p value randoMise is wrong

[Dan White]

We use Gaussian White noise for costes method of p value test. This is same as done in imagej plugin colic test and imaris. Sadly all thre imementations have the same fault : the costes paper makes no mention of White noise as the comparison image. Bitplane say it's an ok approximation. I do not agree at all. There are cases such as busy images where the problem of random overlap is large where a White noise approximation Is nothing like how a proerly psf sized chunk wise randomisation of the image would look. I'm not so sure it's a good approximation for sparse I
ages either. I have seen no mathematical proof that it's a good aproximation yet.

So we must do the image ramdomisation in psf sized chunks as initially described in the original costes paper. The idea is to use the same info in a different order.
More description below.

Costes Statistical Significance Method:

Take one of the image channels, and randomise the spatial location of the information in it. Do this by estimating the size of the point spread function in square pixels (or in voxels for a 3D image), and move chunks of the image of that size to random new location in the image. The spatially randomised image contains the same information as the original, but in a different spatial order. Next measure the Pearson's correlation coefficient r against the image of the other colour channel (which is not randomised, and still virgin). Do this a large number of times (suggest 100) and see what proportion of the randomised images have eaqual or larger r than the original image. This figure is the statistical significance that the observed colocalisation is real. Call this the P-value (actually different to the normal statistical p-value, for some reason). So a P-value of 1 means you are sure that the colocalisation in the original image is real. A P-value of 0.95 (same as p-value = 0.05) means you are 95% sure the observed colocalisation is real and not random, as only 5% of your randomised images had equal or better correlation with the other colour channel image than the original image. This is the usual confidence limit for statistics. Anything lower than 0.95 means that it is likely that the colocalisation you observe is due, at least in part, to random overlap and has nothing to do with any biology.

[Dan White]

the correct method has now been implemented in the Colo_2 Fiji/ImageJ plugin.
basically, take the image, make a list of image blocks of that image, reorder the list using some function like list.randomise, then rebuild the image.
Need a strategy for dealing with ROIs and when the block size does not fit an integer number of times in the image... and out ob bounds method... ie mirror or wrap around is needed.

[Dan White]

see Coloc_2 Fiji plugin code to see how to do this properly. Coastes P value test must be as per tge original article. We can not labe comparison with white noise image as Costes test - as it is not whats in the paper.

[Dan White]

for now, whe I suggest in the original comment would mean extra implementations of new methods, and having done it in the nerw imageJ plugin Colo_2 i now see that this is a hard job. So I suggest to put this off to BXD2 which might reuse the Coloc_2 java code directly.

I will make changes to the GUI text and manual / help that explains that this is an approximation to the Costes test, not the real Costes test. Then at least we are honest.