paul-buerkner/brms

Implementing the Skewed T-Distribution

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#513 opened on Sep 3, 2018

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Description

The skew normal family is great for modeling skewed gaussian data, and the student t distribution is great for outliers. But if one has both skewed data and outliers, the skewed t-distribution might be quite useful! How practical would it be to implement this in brms? This paper outlines an implementation in an MLE/EM setting, but I'm not quite skilled enough to implement it in Stan myself.

https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution#Skewed_t_distribution

Contributor guide

Tech stack
r
Domain
machine learningdata
Issue type
feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
5
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
over 1 week
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
stale
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
needs investigation
Prerequisites
Bayesian statisticsStan modeling languageR programmingbrms package knowledge
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
15
Research direction
This issue requests implementing a skewed T distribution in brms, referencing a paper with an MLE/EM approach but requiring translation to Stan. The contributor should study the provided paper (arXiv:1512.00377) and the Wikipedia article on skewed generalized T distribution, then design a Stan implementation that integrates with brms' family framework. Existing brms implementations of related distributions (e.g., skew normal) can serve as templates. The key challenge is defining the log likelihood and sampling functions in Stan while ensuring numerical stability.