Spatially-dependent Indian Buffet Processes
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912013552189440 |
|---|---|
| author | Sugasawa, Shonosuke Mochihashi, Daichi |
| author_facet | Sugasawa, Shonosuke Mochihashi, Daichi |
| contents | We develop a new stochastic process called spatially-dependent Indian buffet processes (SIBP) for spatially correlated binary matrices and propose general spatial factor models for various multivariate response variables. We introduce spatial dependency through the stick-breaking representation of the original Indian buffet process (IBP) and latent Gaussian process for the logit-transformed breaking proportion to capture underlying spatial correlation. We show that the marginal limiting properties of the number of non-zero entries under SIBP are the same as those in the original IBP, while the joint probability is affected by the spatial correlation. Using binomial expansion and Polya-gamma data augmentation, we provide a novel Gibbs sampling algorithm for posterior computation. The usefulness of the SIBP is demonstrated through simulation studies and two applications for large-dimensional multinomial data of areal dialects and geographical distribution of multiple tree species. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01943 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatially-dependent Indian Buffet Processes Sugasawa, Shonosuke Mochihashi, Daichi Methodology We develop a new stochastic process called spatially-dependent Indian buffet processes (SIBP) for spatially correlated binary matrices and propose general spatial factor models for various multivariate response variables. We introduce spatial dependency through the stick-breaking representation of the original Indian buffet process (IBP) and latent Gaussian process for the logit-transformed breaking proportion to capture underlying spatial correlation. We show that the marginal limiting properties of the number of non-zero entries under SIBP are the same as those in the original IBP, while the joint probability is affected by the spatial correlation. Using binomial expansion and Polya-gamma data augmentation, we provide a novel Gibbs sampling algorithm for posterior computation. The usefulness of the SIBP is demonstrated through simulation studies and two applications for large-dimensional multinomial data of areal dialects and geographical distribution of multiple tree species. |
| title | Spatially-dependent Indian Buffet Processes |
| topic | Methodology |
| url | https://arxiv.org/abs/2409.01943 |