Graphs of cumulative differences and associated variants of the Kolmogorov-Smirnov and Kuiper statistics help gauge calibration or subpopulation deviation without making any particular tradeoff between resolution and statistical confidence (unlike the traditional reliability diagrams and calibration plots), as detailed in
We made some key contributions to clinically accepted acceleration of MRI, building on earlier techniques in deep learning from NYU and the optical illusion that adding noise can sharpen an image -- see, for example, "Why does grain increase acutance?" Errors from our acceleration and diagnostically sound dithering are smaller than the machine errors already present in MRI. Siemens, Philips, GE, and AIRS currently market FDA-approved products based partly on our work as summarized at
Randomization recently revolutionized numerical methods for linear algebra. We have been contributing to many aspects of this movement, especially with regard to improvements important in practice. The key to realizing the widely touted benefits of randomization for the analysis of real, noisy data has turned out to be
Generalizing the fast Fourier transform to families of functions other than the sinusoidal Fourier modes ranges from convenient to critical for many applications, most notably in spectral methods for numerical computations on the sphere. Effective methods (building on others' innovations) for calculations on continuous domains emerged in
Statistical significance testing is due for an overhaul, especially in light of the now widespread availability of modern computers. Our foremost stab at this is the still evolving