Bayesian World View of Cognition

Statistical Machine Learning

Resources

https://rkabacoff.github.io/datavis/

• Power analysis software: https://webpower.psychstat.org/wiki/models/index

General Principles

• Avoid HARKing: Hypothesizing After the Results are Known
• Jamie’s recommendations
  • In the limitation section, talk about what will make you more confident in your statistical anlaysis.
  • For power analysis, focus on the main hypothesis. Don’t try to get enough power for every hypothesis you want to test.

Tips

• Remember to center your predictors
  • (A lesson from a mistake in a “Large-Scale, Multi-Lab” study. https://onlinelibrary.wiley.com/doi/10.1111/desc.70029)
• When there are multiple choices (excluding outliers or not), instead of creating multiple data sheets, create new variables that indicate which treatment of data is used.

Data Preparation

• Use meaningful codes for missing values [1]
• A ‘data dictionary’ that includes the name of each variable, a description, and other information. [1]

Math

• Variance of a random vector $X$ along a direction $u$: $V[u^TX] = u^T V[X] u$
• To derive correlation matries and SS-CP matries
  • Data $X \in \R^{n \times p}$, where n is ther number of observations and p is the number of variables ($x_1 \dots x_p$) → an observation provides pairing of those p values → we can obtain pairwise correlations among these p variables.
  • Variable means (column means) = $\frac{1}{n} \begin{bmatrix} 1 \dots 1\end{bmatrix} X \in \R^{1 \times p}$
  • Mean-centered data $X_c = X - \begin{bmatrix} 1 \dots 1\end{bmatrix}^T \frac{1}{n} \begin{bmatrix} 1 \dots 1\end{bmatrix} X$
  • Sums-of-Squares and Cross-Products matrix (SS-CP) = $X_c^T X_c$
  • Variance-covariance matrix = $\frac{1}{n-1} X_c^T X_c$
  • Correlation matrix = $Diag(1/s_{x_1} \dots 1/s_{x_p}) \frac{1}{n-1} X_c^T X_c Diag(1/s_{x_1} \dots 1/s_{x_p})$

Basics

STAT 400: Statistics and Probability I

• Parameter describes a population; Statistic describes a sample