arXiv 1 Mar 2023 · Statistics — Methodology · publishedPhilosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences (2023) · 13 citations (OpenAlex)
arXiv:2303.00473 · PDF · DOI · OpenAlex · Extracted main text
The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (2020), which is a spike-and-slab shrinkage prior where the spike probability is stochastically increasing and constructed from the stick-breaking representation of a Dirichlet process prior. As a first contribution, this CUSP prior is extended by involving arbitrary stick-breaking representations arising from beta distributions. As a second contribution, we prove that exchangeable spike-and-slab priors, which are popular and widely used in sparse Bayesian factor analysis, can be represented as a finite generalized CUSP prior, which is easily obtained from the decreasing order statistics of the slab probabilities. Hence, exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index in the loading matrix increases, without imposing explicit order constraints on the slab probabilities. An application to sparse Bayesian factor analysis illustrates the usefulness of the findings of this paper. A new exchangeable spike-and-slab shrinkage prior based on the triple gamma prior of Cadonna et al. (2020) is introduced and shown to be helpful for estimating the unknown number of factors in a simulation study.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kowal, D. R. and A. Canale (2022) Semiparametric functional factor models with Bayesian rank selection | 1.000 | 24 | 5 | 100% |
| 2 | Frühwirth-Schnatter, S., D. Hosszejni, and H. F. Lopes (2022) Sparse finite Bayesian factor analysis when the number of factors is unknown | 1.000 | 12 | 5 | 100% |
| 3 | Rocková, V. and E. I. George (2017) Fast Bayesian factor analysis via automatic rotation to sparsity | 1.000 | 7 | 4 | 100% |
| 4 | Legramanti, S., D. Durante, and D. B. Dunson (2020) Bayesian cumulative shrinkage for infinite factorizations | 0.990 | 34 | 8 | 97% |
| 5 | Teh, Y. W., D. Görür, and Z. Ghahramani (2007) Stick-breaking construction for the Indian buffet process | 0.956 | 8 | 4 | 88% |
| 6 | Cadonna, A., S. Frühwirth-Schnatter, and P. Knaus (2020) Triple the gamma – A unifying shrinkage prior for variance and variable selection in sparse state space and TVP models | 0.843 | 3 | 3 | 100% |
| 7 | Heaukulani, C. and D. M. Roy (2020) Gibbs-type Indian Buffet Processes | 0.843 | 3 | 3 | 100% |
| 8 | Ohn, I. and Y. Kim (2022) Posterior Consistency of Factor Dimensionality in High-Dimensional Sparse Factor Models | 0.843 | 3 | 3 | 100% |
| 9 | Ghahramani, Z., T. L. Griffiths, and P. Sollich (2007) Bayesian nonparametric latent feature models (with discussion and rejoinder) | 0.644 | 2 | 2 | 100% |
| 10 | Schiavon, L. and A. Canale (2020) On the truncation criteria in infinite factor models | 0.644 | 2 | 2 | 100% |
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