And optimisation as hubris
Status: draft, last updated 2024-07-20
I’d like to understand when we use randomness in statistics, and why. This post is a placeholder for me figuring that out.
Suppose that we wish to integrate the function \(f: \mathbb{R} \to \mathbb{R}\) over the real line \[ I = \int_{- \infty}^{\infty} f(x) \text{d} x. \] If we are able to generate samples \(x_{1:n} = x_1, \ldots, x_n\) from \(f\) then \(I\) may be estimated using Monte Carlo as \[ \hat I_{\text{MC}} = \frac{1}{n} \sum_{i = 1}^n f(x_i). \] Alternatively, if we are not able to sample directly from \(f\) then we may use importance sampling. If \(y_{1:n}\) are samples from \(g\) then \(I\) may be estimated by \[ \hat I_{\text{IS}} = \frac{1}{n} \sum_{i = 1}^n \frac{f(y_i)}{g(y_i)}. \]
O’Hagan (1987) makes two objections to Monte Carlo…
I'm no expert, but I don't buy that RCTs are the "gold standard". Randomness doesn't magically make control and treatment arms equivalent. Randomness doesn't magically eliminate confounders. Randomness is a fudge to hide, not eliminate, difficult experimental design questions.
— Michael A Osborne (@maosbot) January 11, 2021
For attribution, please cite this work as
Howes (2024, March 28). Adam Howes: Randomisation as modesty. Retrieved from https://athowes.github.io/posts/2024-03-28-randomisation/
BibTeX citation
@misc{howes2024randomisation,
author = {Howes, Adam},
title = {Adam Howes: Randomisation as modesty},
url = {https://athowes.github.io/posts/2024-03-28-randomisation/},
year = {2024}
}