I was just looking for a good explanation of this online to point a lab member towards, and I couldn’t find anything suitable, so I thought I’d write something myself. (Since then, this https://en.wikipedia.org/wiki/Fraction_of_variance_unexplained seems pretty good.

The idea is you have a set of experimental data {Yi} (i=1 to N). These might be responses collected in N different conditions, for example.
The mean is

M = sum{Yi} / N

and the variance about this mean is the total variance

TV = var(Yi) = sum{ (Yi-M)^2 } / N

Now suppose you have some model or fit which predicts values Fi. The residuals between the fit and the data are Ri=(Yi-Fi). The mean of the squared residuals is

RV = sum { (Yi - Fi )^2 } / N

(this is identical to the variance of the residuals if Fi and Yi have the same mean, as they do in linear regression)
The fraction of UNexplained variance is RV/TV, so the fraction of explained variance is 1-RV/TV.

In a perfect world, Fi would be equal to Yi for all i, and therefore these residuals would all be zero. RV=0 and thus all of the variance is explained. The other end of the spectrum is where all the fit values are the same, just equal to the mean of the data: Fi=M. Then we can see from the equations above that RV=TV and none of the variance is explained.

The percentage of variance which is explained is

PV = 100(1-RV/TV).


My colleague Nicholas Port was just asking me about my experience with different versions of Windows & Matlab running Psychophysics Toolbox. I asked my team about their experience, and I thought it might be useful to record their comments here:

Paul: “I used windows 7 and Matlab 2012b for psychophysical experiments before and I didn’t have any issues. However when I was using an Eyelink 1000 (external eyetracker) and timing was important for some reason the functionality only worked on 64 bit, so it is certainly worth considering which version you should use. Windows 7 and 2012A is more than enough.”

Zoltan: “I used Windows 8.1 with Matlab R2014A. I had some issues with timing because the desktop mode is handled differently.
If you do production-quality stuff where timing is important, go with Windows 7 for the time being. I never had any issues with the 64-bit Matlab. However, there is a software limitation with Windows 7: the refresh rate you can set on any monitor is capped at 85 Hz. You will need to do some hacking in the registry if you have a Radeon card, and you can conveniently make a new custom resolution with anything nvidia.
So, currently, the most stable stuff is a Windows 7 PC, 64-bit Matlab, and an nVidia GPU. If you need more power, switch off the swap file, visual effects and have plenty of RAM.”

Ghaith: “I’ve been using PTB on Windows 7 using both 32/64-bit versions of Matlab with no problems.”

Partow: “I had some problems in downloading psychtoolbox with 32-bit on a Windows 7. 64 is fine.”

Back from the Vision Sciences Society meeting; really enjoyed it as ever. The Readlab team had a productive and fun time.

Sid gave a talk about his physiology recordings of V1 neurons in Bruce Cumming’s lab. Zoltan presented a poster about his work using temporal-frequency tagging with disparity in EEG, and Paul gave a poster about how disparity cues influence our perception of size. I gave a poster about ongoing attempts in the lab to decide whether praying mantis vision has distinct spatial frequency channels, a problem which has been engaging lab members Ghaith, Vivek and Lisa as well as long-term collaborator Ignacio Serrano-Pedraza. Ignacio gave a talk about how patching one eye for as little as 2 hrs can result in significant changes in surround suppression, work in collaboration with Holly Bridge down in Oxford.

I’ve just come across the following by Lord Rayleigh, him of the scattering, quoted in The Handbook of Perception and Human Performance:

“In science, by a fiction as remarkable as any to be found in law, what has once been published, even though it be in the Russian language, is spoken of as known, and it is too often forgotten that the rediscovery in the library may be a more difficult and uncertain process than the first discovery in the laboratory.”

Maybe slightly less true today than in 1884, thanks to Google, but still more true than I’d like!

Finally got round to buying a Google Cardboard viewer and trying it out on my HTC One phone. Ooof. That is painful. I don’t know if it’s me or my phone (the magnetic clicker doesn’t work with HTC One, that much I know) but the effect is nauseating. It keeps jumping and skipping even when I don’t move my head. I had to take it off after about two minutes. I hope for the sake of the future of VR that other people aren’t having the same experience as me…

I recently watched “The Machine”, an enjoyable sci-fi flick about a secret defence project to construct an artificially intelligent android who will be the ultimate super-soldier. Naturally, they design their robot killer in the form of a shapely young woman who spends much of the movie in a state of undress. What surprised me was that, in the opening scenes, they manage to totally mess up the well-known Sally-Anne “doll” test for theory of mind.

In the words of Wikipedia, the “the key question [is] the Belief Question: ‘Where will Sally look for her marble?'”. In the movie, the scientist asks “Where should Sally look for her ball?” which makes a nonsense of the whole thing! I am surprised that no one picked up on this in the course of making the movie. Come on people, it’s not rocket science.