Beta Processes

October 14, 2019 — April 8, 2022

linear algebra
Lévy processes
signal processing
sparser than thou
stochastic processes
time series
Figure 1

\[\renewcommand{\var}{\operatorname{Var}} \renewcommand{\corr}{\operatorname{Corr}} \renewcommand{\dd}{\mathrm{d}} \renewcommand{\bb}[1]{\mathbb{#1}} \renewcommand{\vv}[1]{\boldsymbol{#1}} \renewcommand{\rv}[1]{\mathsf{#1}} \renewcommand{\vrv}[1]{\vv{\rv{#1}}} \renewcommand{\disteq}{\stackrel{d}{=}} \renewcommand{\gvn}{\mid} \renewcommand{\Ex}{\mathbb{E}} \renewcommand{\Pr}{\mathbb{P}}\]

An interesting process associated with nonparametric random factor models. Hjort’s Beta process is non decreasing, so it looks like a Lévy subordinator. Is it?

1 References

Hjort. 1992. On Inference in Parametric Survival Data Models.” International Statistical Review / Revue Internationale de Statistique.
Thibaux, and Jordan. 2007. Hierarchical Beta Processes and the Indian Buffet Process.” In Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics.
Wolpert. 2021. Lecture Notes on Stationary Gamma Processes.” arXiv:2106.00087 [Math].