$\newcommand{\a}{\alpha}$$\newcommand{\L}{\mathcal L}$$\newcommand{\one}{\mathbf 1}$$\newcommand{\x}{\mathbf x}$$\newcommand{\0}{\mathbf 0}$Let $G = (V,E)$ be an undirected and unweighted graph on $n$ vertices. I’ll have $A\in\{0,1\}^{n\times…
$\newcommand{\one}{\mathbf 1}$In this post I’m going to consider the following situation: there is a latent unobserved continuous-state Markov chain $Z…
$\newcommand{\e}{\varepsilon}$$\newcommand{\E}{\text{E}}$$\newcommand{\C}{\mathcal C}$$\newcommand{\0}{\mathbf 0}$Consider the linear model $y = X\beta+\e$ with $\E\e = \0$, $\E \e\e^T = \sigma^2 I$, and $X\in\mathbb…
$\newcommand{\e}{\varepsilon}$Suppose I’ve got a linear model $y = X\beta + \e$ with $\e \sim \mathcal N(0, \sigma^2 I)$ and $X\in\mathbb…
$\newcommand{\E}{\text{E}}$$\newcommand{\Var}{\text{Var}}$$\newcommand{\Y}{\mathcal Y}$Here I’m going to introduce Monte Carlo maximum likelihood estimation (MCMLE) and I’ll use it to fit a logistic…
$\newcommand{\x}{\mathbf x}$ In this post I’m going to dust off the shell method from first semester calculus and use it…
$\newcommand{\N}{\mathbb N}$ In this post I’m going to use Euclidean division to do changes of base for nonnegative integers. Euclidean…
In this post I’m going to prove that the following four statements are equivalent given the ZF axioms: (1) Hausdorff…
$\newcommand{\e}{\varepsilon}$In this post I’m going to prove the intermediate value theorem (IVT), Darboux’s theorem, and introduce the Conway base 13…
Here I’m going to go through one common proof of the following result: Theorem: assuming Zorn’s lemma, every vector space…