Characterization of Exponential Families of Lumpable Stochastic Matrices
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_ | 1866908676157079552 |
|---|---|
| author | Watanabe, Shun Wolfer, Geoffrey |
| author_facet | Watanabe, Shun Wolfer, Geoffrey |
| contents | It is known that the set of lumpable Markov chains over a finite state space, with respect to a fixed lumping function, generally does not form an exponential family of stochastic matrices. In this work, we explore efficiently verifiable necessary and sufficient conditions for families of lumpable transition matrices to form exponential families. To this end, we develop a broadly applicable dimension-based method for determining whether a given family of stochastic matrices forms an exponential family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08400 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of Exponential Families of Lumpable Stochastic Matrices Watanabe, Shun Wolfer, Geoffrey Probability Information Theory Statistics Theory It is known that the set of lumpable Markov chains over a finite state space, with respect to a fixed lumping function, generally does not form an exponential family of stochastic matrices. In this work, we explore efficiently verifiable necessary and sufficient conditions for families of lumpable transition matrices to form exponential families. To this end, we develop a broadly applicable dimension-based method for determining whether a given family of stochastic matrices forms an exponential family. |
| title | Characterization of Exponential Families of Lumpable Stochastic Matrices |
| topic | Probability Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2412.08400 |