I’m interested in looking at some spatial mappings between pairs of cortical regions, and believe that these mappings are mediated, to some degree, by the temporal coupling between cortical areas. I don’t necessarily know the functional …
I’m working with some multi-dimensional float-valued data – I’ll call a single instance of this data $X \in \mathbb{R}^{n \times k}$. I have multiple samples $X_{1}, X_{2}…X_{t}$, and want to compare these subspaces – …
The other day, one of my friends and colleagues (I’ll refer to him as “Dr. A”) asked me if I knew anything about assessing biomarker diagnostic power. He went on to describe his clinical problem, which I’ll try to recount here …
Here, we’ll look at various applications of the Delta Method, especially in the context of variance stabilizing transformations, along with looking at the confidence intervals of estimates.
The Delta Method is used as a way to approximate the …
For one of the projects I’m working on, I have an array of multivariate data relating to brain connectivity patterns. Briefly, each brain is represented as a surface mesh, which we represent as a graph $G = (V,E)$, where $V$ is a set of $n$ …
I’m going over Chapter 5 in Casella and Berger’s (CB) “Statistical Inference”, specifically Section 5.5: Convergence Concepts, and wanted to document the topic of convergence in probability with some plots demonstrating the …
In this post, I’m going to briefly cover the relationship between the Poisson distribution and the Multinomial distribution.
Let’s say that we have a set of independent, Poisson-distributed random variables $Y_{1}, Y_{2}… Y_{k}$ …
In my previous post on dynamic mode decomposition, I discussed the foundations of DMD as a means for linearizing a dynamical system123. In this post, I want to look at a way in which we can use rank-updates to incorporate new information into the …
In the next two posts, I want to talk briefly about an algorithm called Dynamic Mode Decomposition (DMD). DMD is a spatiotemporal modal decomposition technique that can be used to identify spatial patterns in a signal (modes), along with the time …
In this post, I’ll be covering the basics of Multivariate Normal Distributions, with special emphasis on deriving the conditional and marginal distributions.
Given a random variable under the usual Gauss-Markov assumptions, with $y_{i} \sim …