Working through the definition of convergence in probability from Casella and Berger, using Chebyshev’s inequality to show the weak law of large numbers for the sample mean and variance, and simulating normal samples to watch both estimates converge.
A sum of independent Poisson variables is Poisson with the summed rate. Conditioned on that sum, the individual counts follow a multinomial distribution.
I modified FSL’s probtrackx2 so streamlines start out heading in a fixed direction into the white matter, which meant reading a lot of poorly documented C++. The post covers why I needed the change and three lessons from it: write meaningful documentation, get comfortable in other people’s code, and don’t dismiss compiled languages.
Translating, rotating, and warping an MRI slice with OpenCV, as a first step toward simulating head motion.
What I took away from Neurohackademy 2018 at the UW eScience Institute. Mostly it was learning how to write software with a team, while building parcellation_fragmenter.
Using rank-one updates to fold new observations into the DMD linear operator without recomputing a full matrix inverse.
An introduction to dynamic mode decomposition, which splits spatiotemporal data into spatial modes and their time dynamics. I derive the algorithm using a truncated SVD, with resting-state MRI as the motivating use case.
Deriving the marginal and conditional distributions of a partitioned multivariate normal.
Using the Sherman-Morrison-Woodbury identity to update a matrix inverse after a low-rank change. The example is updating linear regression coefficients with a new observation without refitting the model.
Deriving each block of the inverse of a 2x2 partitioned matrix using the Schur complements of A and D. I kept running into these identities in a linear models course, including on a midterm.