Statistical tests are complicated because their inventors didn't have computers
11 days ago
- #Monte Carlo
- #statistics
- #hypothesis testing
- Statistical tests are complex due to historical lack of fast computers.
- Monte Carlo simulation can simplify hypothesis testing by brute-forcing p-values.
- Classical tests like Student’s t-test and Kolmogorov-Smirnov test have complicated assumptions and formulas.
- A statistical test requires a null hypothesis, a measurable quantity, and a concrete simulation of the null.
- Example: Computational Student’s t-test compares sheep heights between Wales and New Zealand via simulation.
- Computational power simplifies statistical testing, aligning with the 'bitter lesson' in AI and statistics.
- Chernoff-Hoeffding bounds can convert approximate p-values from simulations into exact ones.