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Month: November 2018

Inferring a hidden Markov chain via MCMC

November 21, 2018 Joseph Leave a comment

$\newcommand{\one}{\mathbf 1}$In this post I’m going to consider the following situation: there is a latent unobserved continuous-state Markov chain $Z…

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Posted in: Linear algebra, Probability, Regression

A column space view of linear regression via the SVD

November 15, 2018 Joseph Leave a comment

$\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…

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Posted in: Linear algebra, Regression

Treating the error variance as a nuisance parameter in linear regression

November 13, 2018 Joseph Leave a comment

$\newcommand{\e}{\varepsilon}$Suppose I’ve got a linear model $y = X\beta + \e$ with $\e \sim \mathcal N(0, \sigma^2 I)$ and $X\in\mathbb…

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Posted in: Probability, Regression

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