vignettes/example-docs/Linear Regression Experiment/docs/dgps/Linear Gaussian DGP.md

In Yu-Group/simChef: Intensive Computational Experiments Made Easy

In the Linear Gaussian DGP, we simulate the feature/design matrix $\mathbf{X} \in \mathbb{R}^{n \times p}$ from a normal distribution and the response vector $\mathbf{y} \in \mathbb{R}^n$ from a linear model. Specifically,

\begin{gather} \mathbf{X} \sim N\left(\mathbf{0}, \begin{pmatrix} 1 & \rho \ \rho & 1 \end{pmatrix}\right), \ \mathbf{y} = \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\epsilon},\ \boldsymbol{\epsilon} \sim N(\mathbf{0}, \sigma^2 \mathbf{I}_n) \end{gather}

Default Parameters in DGP

• Number of samples: $n = 200$
• Number of features: $p = 2$
• Correlation among features: $\rho = 0$
• Amount of noise: $\sigma = 1$
• Coefficients: $\boldsymbol{\beta} = (1, 0)^\top$

[In practice, documentation of DGPs should answer the questions “what” and “why”. That is, “what” is the DGP, and “why” are we using/studying it? As this simulation experiment is a contrived example, we omit the “why” here.]

Yu-Group/simChef documentation built on March 25, 2024, 3:22 a.m.