kimukasetsu
A GP is an intuitive and expressive way to code time covariance in a model. A famous example is the relative birthdays model, discussed by Gelman et al in Bayesian Data Analysis and here [1].
[1] https://avehtari.github.io/casestudies/Birthdays/birthdays.h...
This is called optional stopping and it is not possible using a classic t-test, since Type I and II errors are only valid at a determined sample size. However, other tests make it possible: see safe anytime-valid satistics [1, 2] or, simply, bayesian testing [3, 4].
[1] https://arxiv.org/abs/2210.01948
[2] https://arxiv.org/abs/2011.03567
[3] https://pubmed.ncbi.nlm.nih.gov/24659049/
[4] http://doingbayesiandataanalysis.blogspot.com/2013/11/option...
Multilevel models relax the assumption of independent observations by specifying that the measures of repeated experimental units are dependent on each other. It's a way of telling your model that it has less information than it would have if all observations came from independent units. Therefore, standard errors of effects are usually larger. Otherwise, they are biased [1].
Since most researches are not aware of multilevel models, they design their experiments and aggregate their data to fit the independence assumption, which is rarely a good idea. Many are not even aware of modeling beyond hypothesis tests, and are unable or unwilling to adjust their analysis for confounding factors or non-sampling errors that arise due to experiment design flaws.
Also, p-values should be deprecated, since a) nil hypothesis are strawmen at best and false by definition at worst [2] and b) they incentivize researchers to not think hard about effect sizes and uncertainty in their problems.
[1] https://academic.oup.com/biomet/article/73/1/13/246001 [2] http://www.stat.columbia.edu/~gelman/research/published/fail...
I feel these two things often influence too much the course of Machine Learning research and communities, and this is not good. Most ML researchers and pratictioners are barely aware of the latest advances in parametric modelling, which is a shame. Multilevel models allow you to model response variables with explicit dependent structures. This is done through random (sometimes hierarchical) effects constrained by variance parameters. These parameters regularize the effects themselves and converge really well when fitting factors with high cardinality.
Also, multilevel models are very interesting when it comes to the bias-variance tradeoff. Having more levels in a distribution of random effects actually DECREASES [1] overfitting, which is fascinating.
[1] https://m-clark.github.io/posts/2019-05-14-shrinkage-in-mixe...