Beta Processes

October 14, 2019 — April 8, 2022

algebra
geometry
linear algebra
Lévy processes
measure
probability
signal processing
sparser than thou
stochastic processes
time series

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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].